If 7 men working 7 hrs a day for each of 7 days produce 7 units of work, then the units of

work produced by 5 men working 5 hrs a day for each of 5 days is

🔹1st line:
"If 7 men working 7 hrs a day"​
So, each man works 7 hours/day​
Total men = 7

🔹2nd line:
"for each of 7 days produce 7 units of work,"​
Total work done = 7 units

So, total effort =​

7 men × 7 hrs/day × 7 days = 343 man-hours​
➡ These 343 man-hours produce 7 units of work

So, 1 unit of work = 343 ÷ 7 = 49 man-hours

Ismein "man-hours" ka concept use kiya gaya hai, jo ki work ko measure karne ka ek tareeka hai.

*Man-hours ka matlab hai:*

- Kitne log (men) kitne time tak (hours) kaam karte hain.

*Is example mein:*

- 7 log (men) har din 7 ghante kaam karte hain, aur yeh 7 din tak chalta hai.
- Toh total man-hours = 7 men × 7 hours/day × 7 days = 343 man-hours.

*Aur yeh 343 man-hours kitna kaam karte hain?*

- Ismein likha hai ki yeh 343 man-hours 7 units of work produce karte hain.

*Toh 1 unit of work kitne man-hours mein hota hai?*

- 343 man-hours ÷ 7 units = 49 man-hours per unit.

*Iska matlab hai:*

- 1 unit of work ko complete karne ke liye 49 man-hours lagte hain.

Is tarah se, man-hours ka concept kaam ki quantity aur time ko measure karne mein madad karta hai.

🔹3rd line:
"then the units of work produced by 5 men working 5 hrs a day for each of 5 days is"

Total effort =​
5 men × 5 hrs/day × 5 days = 125 man-hours

Now, divide this total effort by 49 (per unit of work):​

125 ÷ 49 = approx 2.55 units
✅ Final Answer:
The work produced = 125 ÷ 49 = 2.55 units (approx)​
Or, 125/49 units of work (exact fraction).

Both A and B together can complete a work in 20 days and B alone can complete the
same work in 36 days. In how many days will A alone complete the work?

🔸1st Line:
👉
"Both A and B together can complete a work in 20 days"​
Iska matlab:​
A + B ki combined efficiency = 1 work / 20 days​
i.e., A + B = 1/20 work per day

🔸2nd Line:
👉
"B alone can complete the same work in 36 days"​
Toh B ki efficiency = 1 work / 36 days​
i.e., B = 1/36 work per day

🔸3rd Line:
"In how many days will A alone complete the work?"

Ab equation banao:

A + B = 1/20 (B value = 1/36 )

A + 1/36 = 1/20
A = 1/20 - 1/36

🔹 LCM method se solve karo:

LCM of 20 and 36 = 180​
Toh:

1/20 = 9/180
1/36 = 5/180

A = 9/180 - 5/180 = 4/180 = 1/45

👉 A ki efficiency = 1/45 work per day​

Toh A akela 1 kaam karega in 45 days

✅ Final Answer:
A alone will complete the work in 45 days.

Some masons promised to do a work in 10 days but 8 of them were absent and remaining
did the work in 18 days. What was the original number of masons?

🔸1st Line:
"Some masons promised to do a work in 10 days"​

Let assume (some masons) it = x ,​

toh wo milke kaam 10 days mein complete kar lete.

Toh unki total efficiency = x × 10 = 10x man-days​

(Man-days ka matlab: total kaam = log × din)

🔸2nd Line:
👉
"But 8 of them were absent"​
Matlab: Sirf (x – 8) masons aaye kaam par.

🔸3rd Line:
👉
"And remaining did the work in 18 days"​
Toh ab kaam kiya gaya by (x – 8) log in 18 days.​
Total actual man-days = (x – 8) × 18

🔄 Now, set both total work equal:

Original work = 10x​
Work actually done = (x – 8) × 18

So:

10x = (x – 8) × 18

🧮 Solve karo:
Expand RHS:

10x = 18x – 144

Now bring all terms to one side:

10x – 18x = –144

–8x = –144
x = 18

✅ Final Answer:
The original number of masons was 18.

A can do a certain work in the same time as B and C together can do. If A and B together
can do the work in 8 days and C alone can do the same work in 40 days, in how many
days will B alone do the same work?

Chaliye is question ko line by line aur step-by-step samajhte hain, jaise khud ko samjha rahe
ho:

🔹 1st Line:
➡️
"A can do a certain work in the same time as B and C together can do."​
A ki efficiency = B + C ki efficiency​
(Matlab A ka kaam karne ka speed B aur C dono ke barabar hai)
🔹 2nd Line:
➡️
"If A and B together can do the work in 8 days"​
A + B = 1/8 work per day​
(Yaani A aur B milke 1 din mein 1/8 kaam karte hain)

🔹 3rd Line:
➡️
"C alone can do the same work in 40 days"​
C = 1/40 work per day

Equation form :

A + B = ⅛ ( use : A = B + C , C = ¼)

B + 1/40 + B = ⅛

2B + 1/40 = 1/8

2B = 1/8 - 1/40

2B = (5 - 1) / 40

2B = 4 / 40

2B = 1 / 10

B = 1 / 20

✅ Final Answer:
B alone will do the work in 20 days.

If 10 men working for 6 hours per day can complete a piece of work in 90 days, in how
many days will 6 men working for 15 hours per day complete the same piece of work?

🔹 1st line:
"If 10 men working for 6 hours per day"

👉 Okay! 10 aadmi hain, aur har din 6 ghante kaam karte hain.​
Toh 1 din ka total effort = 10 men × 6 hours = 60 man-hours per day
🔹 2nd line:
"can complete a piece of work in 90 days"

👉 Toh total work = 60 man-hours/day × 90 days = 5400 man-hours

This is fixed total work. Yahi work hume second case mein karwana hai.

🔹 3rd line:
"in how many days will 6 men working for 15 hours per day complete the same piece of
work?"

👉 Let’s calculate their daily effort:​

6 men × 15 hours = 90 man-hours/day

Ab simple formula lagate hain:

Total Work ÷ Daily Effort = Number of Days

So:

5400 man-hours ÷ 90 man-hours/day = 60 days

✅ Final Answer: 60 days

19 - 6 - 2025
24 persons working 8 hours a day can complete 2 units of a work in 10 days. How many
persons are required to complete 4 units of that work, if they work 6 hours a day for 16
days ?

🔹 1st line:
👉
"24 persons working 8 hrs/day can complete 2 units in 10 days."​

👉
Total effort = 24 × 8 × 10 = 1920 hours → for 2 units​
So, 1 unit = 1920 ÷ 2 = 960 hours
🔹 2nd line:
👉
"How many persons for 4 units,"​
Total work = 960 × 4 = 3840 hours

🔹 3rd line:
👉
"if they work 6 hrs/day for 16 days?"​
Let required persons = x​
Then, total effort = x × 6 × 16 = 96x hours

🔹 Now solve:
96x = 3840​
x = 3840 ÷ 96 = 40

✅ Final Answer: 40 persons

18 persons working 8 hours a day can complete 3 units of works in 10 days. How many
persons are required to complete 5 units of that work in 16 days working 6 hours a day?

🔹 1st line:
"18 persons working 8 hrs/day complete 3 units in 10 days."

👉 Total effort = 18 × 8 × 10 = 1440 hours​

👉 This is for 3 units, so:​
1 unit = 1440 ÷ 3 = 480 hours

🔹 2nd line:
"How many persons for 5 units?"

👉 Total work = 480 × 5 = 2400 hours

🔹 3rd line:
👉
"Work to be done in 16 days, working 6 hrs/day."​
Let required persons = x​
Total effort available = x × 6 × 16 = 96x hours

🔹 Now solve:
96x = 2400​
x = 2400 ÷ 96 = 25

✅ Final Answer: 25 persons

To do a certain work, A and B work on alternate days, with B beginning the work on the
first day. A can finish the work alone in 48 days. If the work gets completed in 11 ⅓ days,
then B alone can finish 4 times the same work in:

A is as efficient as B and C together. Working together A and B can complete a work in 36

days and C alone can complete it in 60 days. A and C work together for 10 days. B alone
will com-plete the remaining work in :

🔹 1st line:
➡️
A is as efficient as B and C together.​
That means:​
A = B + C (in work efficiency per day)

🔹 2nd line:
➡️
A and B together can complete the work in 36 days​
So A + B’s 1 day work = 1/36
🔹 Now use A = B + C in the above:
A + B = (B + C) + B = 2B + C

So,​

➖ (Equation ①)
(2B + C)’s 1 day work = 1/36​
→ Equation: 2B + C = 1/36

🔹 3rd line:
➡️
C alone can complete the work in 60 days​
So C's 1 day work = 1/60

Now put C = 1/60 in Equation ①:​

2B + 1/60 = 1/36​
→ Subtract 1/60:​
2B = 1/36 - 1/60​
LCM = 180:​
→ 2B = (5 - 3)/180 = 2/180 = 1/90​
→ So B’s 1 day work = 1/180

🔹 Now find A’s 1 day work:

From A = B + C​
= 1/180 + 1/60 = (1 + 3)/180 = 4/180 = 2/90 = 1/45

So A's 1 day work = 1/45

🔹 4th line:
A and C work together for 10 days​
→ A + C’s 1 day work = 1/45 + 1/60 = (4 + 3)/180 = 7/180​
→ In 10 days:​
Work done = 10 × 7/180 = 70/180 = 7/18

🔹 Work left = 1 - 7/18 = 11/18

🔹 5th line:
B alone will do the remaining 11/18 work.​
→ B’s 1 day work = 1/180

So time = (11/18) ÷ (1/180) =​

= 11/18 × 180/1 = 110

✅ Final Answer: 110 days

B alone will complete the remaining work in... ke liye formula hai:
Time = Remaining Work / B's Efficiency

Jahan:
- Remaining Work = Kaam jo abhi baki hai
- B's Efficiency = B ki kaam karne ki dar

Is formula ko use karke hum B ke liye time nikal sakte hain.

Time = (11/18) / (1/180)

= (11/18) × (180/1)
= 110

Toh, B alone will complete the remaining work in 110 days.

A. B and C can finish a task in 42 days, 84 days and 28 days, respectively. A started the
work B joined him after 3 days. If C Joined them after 5 days from the beginning, then for
many days did A work till the completion of the task?

✅ 1st line (Question info):

A, B, C finish task in 42, 84, and 28 days.

Unka 1 day ka kaam:

●​ A = 1/42
●​ B = 1/84
●​ C = 1/28

✅ 2nd line (Question):

A started the work. B joined after 3 days.​
→ Pehle 3 din: sirf A ka kaam​
= 3 × (1/42) = 3/42 = 1/14 work done

✅ 3rd line (Question):

C joined after 5 days.

●​ Pehle 3 din: A alone

●​ Agle 2 din (4th & 5th): A + B​
= 2 × (1/42 + 1/84)​
= 2 × (2 + 1)/84 = 2 × 3/84 = 6/84 = 1/14 work

Ab total work after 5 days =​

1/14 (A alone) + 1/14 (A + B) = 2/14 = 1/7 work

✅ 4th line (Question):

C joined from 6th day onwards.

Ab kaam ho chuka hai = 1/7​

Bacha hua work = 1 - 1/7 = 6/7

Ab kaam kar rahe hain A + B + C: = 1/42 + 1/84 + 1/28​

LCM = 168​
→ (4 + 2 + 6)/168 = 12/168 = 1/14 per day

So remaining 6/7 work karein 1/14 per day se:​

Time = (6/7) ÷ (1/14) = (6/7) × 14 = 12 days

✅ Final Answer (Total A ka kaam):

●​ A ne kaam kiya:​
= 3 days (alone) + 2 days (with B) + 12 days (with B & C)​
= 17 days

✅ Answer: A worked for 17 days.

A and B together can do a plece of work in 10 days, B and C to gether can do it in 15 days
while C and A together can do it in 20 days. They work together for 8 days. C alone will
complete the remaining work in :

Let’s solve this line-by-line, in simple steps:

🔹 1st line:
A + B can do work in 10 days​
So, their 1-day work = 1/10

🔹 2nd line:
B + C can do it in 15 days​
So, their 1-day work = 1/15

🔹 3rd line:
C + A can do it in 20 days​
So, their 1-day work = 1/20

💡 Add all three equations:

(A + B) + (B + C) + (C + A) = 1/10 + 1/15 + 1/20​
→ 2A + 2B + 2C = LCM(10,15,20) = 60​
→ 1/10 + 1/15 + 1/20 = (6 + 4 + 3)/60 = 13/60​
So,​
2(A + B + C) = 13/60​
⇒ A + B + C = 13/120

🔹 4th line:
They work together for 8 days

So, total work done = 8 × 13/120 = 104/120 = 26/30 = 13/15

🔹 Remaining work = 1 – 13/15 = 2/15

🔹 Now C alone will complete the rest
We need C's 1-day work.

We already know:

●​ A + B = 1/10
●​ A + B + C = 13/120​
⇒ So, C = (13/120) – (1/10) = (13 – 12)/120 = 1/120

🔚 Now time = (Remaining work) ÷ (C’s 1-day work)

= (2/15) ÷ (1/120) = (2/15) × 120 = 16 days

✅ Final Answer: 16 days

18 men can complete a work in 9 days. After they have worked for 5 days, 6 more men
join them How Many days will they take to complete the remaining work?

Let’s solve it line by line in simple steps:

🔹 1st line:
18 men can complete the work in 9 days​
So, total work = 18 men × 9 days = 162 man-days

🔹 2nd line:
They work for 5 days with 18 men​
→ Work done = 18 × 5 = 90 man-days

🔹 Remaining work = 162 – 90 = 72 man-days

🔹 3rd line:
Now 6 more men join → Total = 18 + 6 = 24 men

🔹 4th line:
Now we have 72 man-days of work and 24 men.​
So, days required = 72 ÷ 24 = 3 days

✅ Final Answer: 3 days

A, B and C can complete a piece of work in 4, 28 and 56 days respectively. Working
together they can complete the same work in how many days?

🔹 1st line:
A can complete the work in 4 days​
So, A's 1 day work = 1/4

🔹 2nd line:
B can complete it in 28 days​
So, B's 1 day work = 1/28

🔹 3rd line:
C can complete it in 56 days​
So, C's 1 day work = 1/56
🔹 4th line:
All three working together =​
A + B + C's 1 day work =​
= 1/4 + 1/28 + 1/56

🔹 Let’s take LCM of 4, 28, and 56 = 56

Now,

●​ 1/4 = 14/56
●​ 1/28 = 2/56
●​ 1/56 = 1/56

Total = 14 + 2 + 1 = 17/56

🔹 Total work = 1
So, number of days to complete the work =​
1 ÷ (17/56) = 56/17

= 3 5/17

✅ Final Answer: 56/17 days or approx. 3.29 days

If 16 men working 12 hours a day can complete a work in 27 days, then working for how
many hours a day can 18 men complete the work in 24 days?

🔹 1st line:
"If 16 men working 12 hours a day can complete a work in 27 days,"

👉 Total work = men × hours per day × number of days​

= 16 × 12 × 27 = 5184 man-hours
🔹 2nd line:
"then working for how many hours a day can 18 men complete the work in 24 days?"

👉 Hume naya "hours per day" (x) nikalna hai, jab:​

men = 18,​
days = 24

Toh naya work bhi 5184 hoga:

18 × x × 24 = 5184

Ab solve karte hain:

→ 432x = 5184​
→ x = 5184 ÷ 432 = 12 hours

✅ Final Answer: 12 hours per day

A and B can complete a task in 25 days. B alone can complete 33 ⅓ % of the same task in
15 days. In how many days can A alone complete 4/15 th of the same task?

🔹 1st line:
👉
"A and B can complete a task in 25 days."​
Dono milke 1 day mein 1/25 work karte hain.

🔹 2nd line:
"B alone can complete 33⅓% of the same task in 15 days."

👉
33⅓% = 1/3 of the task​
B does 1/3 work in 15 days,​
So full work ke liye B ko chahiye:

15 × 3 = 45 days​
→ B’s 1-day work = 1/45
🔹 Now, find A’s 1-day work:
We know:​
A + B = 1/25 per day (Use : B = 1/45 )

A + 1/45 = 1/25​
A = 1/25 − 1/45

Take LCM (LCM of 25 and 45 = 225):

→ A = (9 − 5)/225 = 4/225

So A alone does 4/225 work in 1 day.

🔹 Final line:
"In how many days can A alone complete 4/15 of the same task?"

Use formula:​
Time = Work ÷ Rate

→ Work = 4/15​
→ Rate = 4/225

So:

Time = (4/15) ÷ (4/225) = 225/15 = 15 days

✅ Final Answer: 15 days

20 - 6 - 2025
X alone can do a certain work in 15 days. Y alone can do the same work in 30 days. X, Y
and Z to-gether can do the same work in 9 days. In how many days will Z alone do the
same work?

🔹 1st line:
👉
"X alone can do a certain work in 15 days."​
So, X's 1-day work = 1/15
🔹 2nd line:
👉
"Y alone can do the same work in 30 days."​
So, Y's 1-day work = 1/30

🔹 3rd line:
👉
"X, Y and Z together can do the same work in 9 days."​
So, (X + Y + Z)'s 1-day work = 1/9

✅ Step 1: Add X and Y’s 1-day work

X + Y + Z = 1/9

1/15 + 1/30 + z = 1/9

Lcm = 30

1/30 + 1/30 = 1/9

2/ 30 + 1 /30 + z = 1/9

3 /30 + z = 1/9

1/10 + z = 1/9

Z = 1/9 - 1/10

Lcm = 90

Z = 10/90 - 9 / 90

Z = 1 / 90

✅ Final Answer:
Z alone can do the work in 90 days.
 Reciprocal Rule

Jab hum equation mein 1/10 ko dusri taraf le jaate hain, toh hum usse subtract ya add karte hain, na ki multiply ya divide.

Is case mein:
1/10 + z = 1/9

Dono taraf se 1/10 subtract karne par:

z = 1/9 - 1/10

Yahan 1/10 ka sign change hota hai, lekin woh reciprocal nahi hota.

Reciprocal tab hota hai jab hum division ko multiplication mein badalte hain, jaise:
x ÷ 1/10 = x × 10

Lekin addition aur subtraction mein, sign change hota hai, reciprocal nahi.

A man can finish a piece of work in 15 days. A women can com-plete the same work in 10
days. Both work together for 5 days, then the man leaves. How many days will be taken
by the woman to finish the remaining work?

🔹 1st line:
👉
"A man can finish a piece of work in 15 days."​
So, man’s 1 day work = 1/15

🔹 2nd line:
👉
"A woman can complete the same work in 10 days."​
So, woman’s 1 day work = 1/10

🔹 3rd line:
👉
"Both work together for 5 days,"​
Together in 1 day:​
= 1/15 + 1/10​
= (2 + 3)/30 = 5/30 = 1/6

👉 Work done in 5 days =​

5 × 1/6 = 5/6

🔹 4th line:
"then the man leaves. How many days will be taken by the woman to finish the remaining
work?"

👉 Total work = 1​
👉 Work left = 1 - 5/6 = 1/6
👉 Woman's 1-day work = 1/10​
So, days needed =​
= (1/6) ÷ (1/10)​
= 10/6 = 5/3 = 1⅔ days

✅ Final Answer:
1⅔ days (i.e. 1 day and 4 hours) will be taken by the woman to finish the remaining work.

Samrat alone can complete a work in 10 days and Virat alone can complete the same
work in 40 days. If they are working on alternate days with Samrat the work, then in how
many days will the total work be completed?

Sure. Let’s solve step by step, line by line:

🟩 1st line:
👉
"Samrat alone can complete a work in 10 days"​
Samrat's 1 day work = 1/10

🟩 2nd line:
👉
"Virat alone can complete the same work in 40 days."​
Virat's 1 day work = 1/40

🟩 3rd line:
👉
"If they are working on alternate days with Samrat starting the work,"​
So:
 ●​ Day 1: Samrat → 1/10
●​ Day 2: Virat → 1/40
●​ Total in 2 days = 1/10 + 1/40 = (4 + 1)/40 = 5/40 = 1/8

🟩 4th line:
👉
"Then in how many days will the total work be completed?"​
Every 2 days = 1/8 work

Toh pura kaam (1 unit) hone ke liye:

👉 1 ÷ (1/8) = 8 cycles (of 2 days)

👉 8 × 2 = 16 days
✅ Answer: 16 days full work done
Vishal alone can complete 1/3 part of a work in 60 days and Ashok alone can complete
1/4 part of the same work 30 days. In how many days Vishal and Ashok together can
complete the same work?

🟩 1st line:
"Vishal alone can complete 1/3 part of a work"

🟩 2nd line:
➡️
"in 60 days"​
Vishal takes 60 days for 1/3 work,​
So full work = 60 × 3 = 180 days​
👉 Vishal's 1-day work = 1/180

🟩 3rd line:
"Ashok alone can complete 1/4 part of the same work"
🟩 4th line:
➡️
"in 30 days."​
Ashok takes 30 days for 1/4 work​
So full work = 30 × 4 = 120 days​
👉 Ashok's 1-day work = 1/120

🟩 5th line:
"In how many days Vishal and Ashok together can complete the same work?"​
Together 1-day work = 1/180 + 1/120​
LCM of 180 and 120 = 360​
= 2/360 + 3/360 = 5/360 = 1/72​
➡️ They will complete the work in 72 days

✅ Answer: 72 days
If 10 men can complete a piece of work in 12 days by working 7 hours a day, then in how
many days can 14 men do the same work by working 6 hours a day?

🟩 1st line:
"If 10 men can complete a piece of work in 12 days by working 7 hours a day,"

➡ Total work =​
10 men × 12 days × 7 hrs = 840 man-hours

🟩 2nd line:
"then in how many days can 14 men do the same work by working 6 hours a day?"

Let required days = x​

➡ New total effort =​
14 men × x days × 6 hrs = 840​
→ 84x = 840​
→ x = 10
✅ Answer: 10 days
A can do 4/5 th of a work in 20 days and B can do ¾ th of the same work in 15 days. They
work together for 10 days. C alone completes the remaining work in 1 day. B and C
together can complete ¾ th of the same work in :

🟩 1st line:
"A can do 4/5 of a work in 20 days"​
➡ So, total work = 20 ÷ (4/5) = 25 days (A can do full work in 25 days)​
➡ A’s 1 day work = 1/25

🟩 2nd line:
"B can do 3/4 of the same work in 15 days"​
➡ Total work = 15 ÷ (3/4) = 20 days (B can do full work in 20 days)​
➡ B’s 1 day work = 1/20

🟩 3rd line:
"They work together for 10 days."​
Work done by A + B in 1 day = 1/25 + 1/20 = (4 + 5)/100 = 9/100​
➡ In 10 days, they do: 10 × 9/100 = 90/100 = 9/10 work

🟩 4th line:
"C alone completes the remaining work in 1 day."​
Remaining work = 1 - 9/10 = 1/10​
➡ C’s 1 day work = 1/10

🟩 5th line:
"B and C together can complete 3/4 of the same work in:"​
B’s 1 day work = 1/20, C’s 1 day work = 1/10​
Combined = 1/20 + 1/10 = (1 + 2)/20 = 3/20​
➡ Time = Work ÷ Rate = (3/4) ÷ (3/20) = (3/4) × (20/3) = 5

✅ Answer: 5 days
A and B together can do a cer-tain work in x days. Working alone, A and B can do the
same work in (x+8) and (x+18) days respectively. A and B together will complete 5 /6 th of
the same work in:

🟩 1st line:
"A and B together can do the work in x days"​
➡ A + B's 1-day work = 1/x

🟩 2nd line:
"A alone in (x+8) days, B alone in (x+18) days"​
➡ A's 1-day work = 1/(x+8)​
➡ B's 1-day work = 1/(x+18)

So,​
1/(x+8) + 1/(x+18) = 1/x

📌 Take LCM of all terms and solve:​

Multiply both sides by x(x+8)(x+18)

x(x+18) + x(x+8) = (x+8)(x+18)

x² + 18x + x² + 8x = x² + 26x + 144

2x² + 26x = x² + 26x + 144

⇒ x² = 144 ⇒ x = 12
🟩 3rd line:
"A and B together will complete 5/6 of the same work in:"​
A + B do full work in x = 12 days​
➡ So, time for 5/6 work = 12 × 5/6 = 10 days

✅ Answer: 10 days
A can complete one-third part of a work in 5 days, B can do two-fifith part of the same
work in 10 days and C can do 75% of the same work in 15 days. They work together for 6
days. In how many days will B alone complete the remaining work?

✅ 1st line:
"A can complete 1/3 of work in 5 days"​
➡ Full work by A = 5 × 3 = 15 days​
➡ A's 1-day work = 1/15

✅ 2nd line:
"B can do 2/5 of work in 10 days"​
➡ Full work by B = 10 × (5/2) = 25 days​
➡ B's 1-day work = 1/25

✅ 3rd line:
"C can do 75% (i.e. 3/4) of work in 15 days"​
➡ Full work by C = 15 × (4/3) = 20 days​
➡ C's 1-day work = 1/20

✅ 4th line:
"They work together for 6 days"​
➡ A + B + C’s 1-day work =​
1/15 + 1/25 + 1/20​
LCM = 300​
→ (20 + 12 + 15)/300 = 47/300

➡ Work done in 6 days = 6 × 47/300 = 282/300 = 47/50

✅ 5th line:
Remaining work = 1 − 47/50 = 3/50​
B alone's 1-day work = 1/25​
➡ Time = (3/50) ÷ (1/25) = (3/50) × 25 = 3/2 = 1.5 days

✅ Final Answer: 1.5 days or 1 day 12 hours

75% ko fraction mein badalne ke liye:
75% = 75/100
= 3/4 (simplified)

Isliye, 75% = 3/4 hota hai.

Yeh simplification is prakaar hai:

75 ÷ 25 = 3
100 ÷ 25 = 4

Isliye, 75/100 = ¾.

Dono same hai

A can complete one-third part of a work in 5 days, B can do two-fifith part of the same
work in 10 days and C can do 75% of the same work in 15 days. They work together for 6
days. In how many days will B alone complete the remaining work?

✅ 1st line:
"A can complete one-third part of a work in 5 days"​
➡ So, full work = 5 × 3 = 15 days​
➡ A's 1-day work = 1/15

✅ 2nd line:
"B can do two-fifth part in 10 days"​
➡ Full work = 10 × (5/2) = 25 days​
➡ B's 1-day work = 1/25

✅ 3rd line:
"C can do 75% (i.e. 3/4) of work in 15 days"​
➡ Full work = 15 × (4/3) = 20 days​
➡ C's 1-day work = 1/20

✅ 4th line:
They work together for 6 days​
➡ Combined 1-day work =​
1/15 + 1/25 + 1/20​
LCM of 15, 25, 20 = 300​
→ (20 + 12 + 15)/300 = 47/300

➡ Work done in 6 days = 6 × 47/300 = 282/300 = 47/50

✅ 5th line:
Remaining work = 1 − 47/50 = 3/50​
B’s 1-day work = 1/25

➡ Time = (3/50) ÷ (1/25) =

= 3 / 50 × 25 /1

= 75/50

= 3/2 Ans : 1 1/2

✅ Final Answer:
B alone will complete the remaining work in 1 1/2 days
A and B, working together, can complete work in d days. Working alone, A takes (8 + d)
days and B takes (18 + d) days to complete the same work. A works for 4 days. The
remaining work will be completed by B alone, in:

Amit and Sunil together can com-plete a work in 9 days. Sunil and Dinesh together can
complete the same work in 12 days, and Amit and Dinesh together can complete the
same work in 18 days. In how many days will they complete the work if Amit, Sunil and
Dinesh work together?

✅ 1st line:
Amit + Sunil = 9 days​
⇒ Work per day = 1/9

✅ 2nd line:
Sunil + Dinesh = 12 days​
⇒ Work per day = 1/12

✅ 3rd line:
Amit + Dinesh = 18 days​
⇒ Work per day = 1/18

Add all three equations:

(A + S) + (S + D) + (A + D)​
= 2A + 2S + 2D​
= 1/9 + 1/12 + 1/18

Take LCM of 9, 12, 18 = 72​

→ (8 + 6 + 4)/72 = 18/72 = 1/4

So:​
2(A + S + D) = 1/4​
⇒ A + S + D = 1/8
✅ Final Answer:
All three together will complete the work in 8 days

A can do 1/ 3 of a work in 30 days. B can do 2/5 of the same work in 24 days. They
worked together for 20 days. C completed the remaining work in 8 days. Working
together A, B and C will complete the same work in :

✅ 1st line:
A can do 1/3 work in 30 days​
→ Full work = 30 × 3 = 90 days​
→ A’s 1-day work = 1/90

✅ 2nd line:
B can do 2/5 work in 24 days​
→ Full work = 24 × 5/2 = 60 days​
→ B’s 1-day work = 1/60

✅ 3rd line:
A and B work together for 20 days​
→ Work done = 20 × (1/90 + 1/60)

LCM of 90 and 60 = 180​

= 20 × (2 + 3)/180 = 20 × 5/180 = 100/180 = 5/9 work done

✅ 4th line:
C does the remaining work in 8 days​
→ Remaining = 1 − 5/9 = 4/9​
→ C’s 1-day work = 4/9 ÷ 8 = 1/18

✅ 5th line:
A + B + C = 1/90 + 1/60 + 1/18​
LCM of 90, 60, 18 = 180​
= (2 + 3 + 10)/180 = 15/180 = 1/12

✅ Final Answer:
A, B and C together will complete the work in 12 days ✅
A and B can do a job in 10 days and 5 days, respectively. They worked together for two
days, after which B was replaced by C and the work was finished in the next three days.
How long will C alone take to finish 60% of the job?

✅ 1st line:
A can do the job in 10 days ⇒ A's 1-day work = 1/10​
B can do it in 5 days ⇒ B's 1-day work = 1/5

✅ 2nd line:
A and B worked together for 2 days​
→ Work done = 2 × (1/10 + 1/5)​
= 2 × (1/10 + 2/10) = 2 × 3/10 = 6/10 = 3/5

✅ 3rd line:
B is replaced by C; A and C finish the remaining work in 3 days​
Remaining work = 1 − 3/5 = 2/5

Let C's 1-day work = 1/x​

A’s 1-day work = 1/10​
→ A + C’s 1-day work = 1/10 + 1/x​
→ In 3 days:​
3 × (1/10 + 1/x) = 2/5

✅ Solve the equation:

Multiply both sides by 5:​
→ 15 × (1/10 + 1/x) = 2​
→ 3/2 + 15/x = 2​
→ 15/x = 2 − 3/2 = 1/2​
→ x = 30

✅ So, C alone can do the full work in 30 days

✅ 5th line:
C alone takes 30 days to complete full work​
→ To finish 60% of the job = 60% of 30 = 18 days

✅ Final Answer:
C will take 18 days to finish 60% of the job. ✅
🟡🤷 21 - 6 - 2025 🤷🟡
A and B can do a piece of work in 25 days. B alone can do 66 2/3% of the same work in 30
days. In how many days can A alone do 4/15 part of the same work?

✅ 1st line:
A and B can do the work in 25 days​
→ A + B’s 1-day work = 1/25

✅ 2nd line:
B alone can do 66 2/3% = 2/3 of work in 30 days​
→ So, B’s 2/3 work = 30 days​
→ 1 full work = 30 × (3/2) = 45 days​
→ So, B’s 1-day work = 1/45

Now use: A + B = 1/25 and B = 1/45​

→ A’s 1-day work = 1/25 − 1/45​
LCM of 25 and 45 = 225​
→ = (9 − 5)/225 = 4/225

✅ 3rd line:
Time taken by A to do 4/15 work​
→ Time = (4/15) ÷ (4/225) =​
= (4/15) × (225/4) = 225 / 15 = 15 days

✅ Final Answer:
A alone will take 15 days to do 4/15 of the work

A can do 33 ⅓ % of a work in 10 days and B can do 66 ⅔% of the same work in 8 days.

Both worked together for 8 days. C alone completed the remaining work in 3 days. A and
C together will complete 5/6 part of the original work in:

✅ 1st line:
A can do 33⅓% of a work in 10 days​
→ 33⅓% = 1/3 of the work​
→ A’s 1-day work = (1/3) ÷ 10 = 1/30 (A’s 1-day work)

✅ 2nd line:
B can do 66⅔% of the same work in 8 days​
→ 66⅔% = 2/3 of the work​
→ B’s 1-day work = (2/3) ÷ 8 = 1/12 (B’s 1-day work)

✅ 3rd line:
Both A and B worked together for 8 days​
→ A and B together’s 1-day work = 1/30 + 1/12​
→ LCM of 30 and 12 = 60​
→ A and B’s 1-day work = (2/60 + 5/60) = 7/60​
→ Work done by A and B in 8 days = 8 × 7/60 = 56/60 = 14/15 of the work

✅ 4th line:
C alone completed the remaining work in 3 days​
→ Remaining work = 1 − 14/15 = 1/15​
→ C’s 1-day work = (1/15) ÷ 3 = 1/45 (C’s 1-day work)

✅ 5th line:
A and C together will complete 5/6 part of the original work​
→ A + C’s 1-day work = 1/30 + 1/45​
→ LCM of 30 and 45 = 90​
→ A + C’s 1-day work = (3/90 + 2/90) = 5/90 = 1/18​
→ Time taken to complete 5/6 of the work = (5/6) ÷ (1/18) = 15 days

✅ Final Answer:
A and C together will complete 5/6 part of the work in 15 days. ✅
25 women can do a piece of work in 60 days. After how many days from the start of the
work should 15 more women join them so that the work is done in 45 days?

🟠 1st line: 25 women can do a piece of work in 60 days.

🟢 That means:
Total work = 25 women × 60 days = 1500 woman-days
🟠 2nd line: After how many days from the start of the work should 15 more women join
them

Let’s say, after x days, 15 more women join.​

So for the first x days, only 25 women work.

🟢 Work done in x days = 25 × x = 25x woman-days

Pehle x dinon mein, 25 mahilaein kaam karti hain.

Work done by 25 women in x days = 25x woman-days.

Baaki (45 - x) dinon mein, 40 mahilaein (25 + 15) kaam karti hain.

🟠 3rd line: So that the work is done in 45 days

Total time = 45 days​
So, remaining days = 45 − x​
Now 25 + 15 = 40 women work for (45 − x) days

🟢 Work done = 40 × (45 − x) = 40(45 − x)

🔷 Total work = Work before + Work after

So,

25x + 40(45 − x) = 1500

Let’s solve:

25x + 1800 − 40x = 1500​

−15x = 1500 − 1800​
−15x = −300​
x = 20

✅ Final Answer:
15 more women should join after 20 days from the start.
A, B and C together can com-plete a work in x, 30 and 45 days, respectively. B and C
worked together for 6 days. The remaining work was completed by A alone in 12 days.
The value of x is.

Let's solve line by line — clean and clear:

✅ 1st line:
A, B and C together can complete a work in x, 30 and 45 days, respectively.​
That means:

●​ A’s 1 day work = 1/x

●​ B’s 1 day work = 1/30
●​ C’s 1 day work = 1/45

✅ 2nd line:
👉
B and C worked together for 6 days​
B + C’s 1 day work =​
LCM of 30 and 45 = 90​
= (3 + 2)/90 = 5/90 = 1/18​
So, in 6 days:​
6 × (1/18) = 1/3 work done

✅ 3rd line:
Remaining work (1 − 1/3) = 2/3​
This was done by A in 12 days​
So, A’s 1 day work = (2/3) ÷ 12 = 2 / (3×12) = 1/18

✅ 4th line:
A’s 1 day work = 1/x = 1/18​
So, x = 18

1/x aur 1/18 dono equal hain, isliye x ka maan seedhe 18 hota hai.
✅ Final Answer: x = 18 days
40 persons take 6 days to com-plete a certain task, working 10 hours a day. How many
hours a day will be sufficient for 30 per-sons to complete the same task In 10 days?

Let's solve it sentence by sentence in less words and clean logic:

✅ 1st line:
40 persons take 6 days to complete a certain task, working 10 hours a day.​
Total work =​
40 × 6 × 10 = 2400 man-hours

✅ 2nd line:
How many hours/day will be sufficient for 30 persons

✅ 3rd line:
to complete the same task in 10 days​
Let required hours/day = x​
So,​
30 × 10 × x = 2400​
→ 300x = 2400​
→ x = 2400 ÷ 300 = 8

✅ Final Answer: 8 hours/day

A can finish a piece of the work in 16 days and B can finish it in 12 days. They worked
together for 4 days and then A left. B fin-ished the remaining work. For how many total
number of days did B work to finish the work completely?

✅ 1st line:
A can finish in 16 days ⇒ A's 1 day work = 1/16​
B can finish in 12 days ⇒ B's 1 day work = 1/12
✅ 2nd line:
They worked together for 4 days​
Total work in 4 days =​
4 × (1/16 + 1/12)​
= 4 × (7/48)​
= 28/48 = 7/12 work done

✅ 3rd line:
Remaining work = 1 − 7/12 = 5/12​
B alone finished it ⇒ Time = (5/12) ÷ (1/12) = 5 days

✅ 4th line — Final Answer:

B worked total = 4 days (with A) + 5 days (alone) = 9 days ✅
A, B and C can do a work in 8, 10 and 12 days, respectively. After completing the work
to-gether, they received Rs. 5,550. What is the share of B (in Rs.) in the amount received?

🟩 1st line:
A, B, C complete work in 8, 10, 12 days respectively​
→ Take LCM of 8, 10, 12 = 120 units (Total work)

Their 1-day work:​

A = 120 ÷ 8 = 15 units/day​
B = 120 ÷ 10 = 12 units/day​
C = 120 ÷ 12 = 10 units/day

🟩 2nd line:
Total amount received = ₹5550

🟩 3rd line:
Find B’s share​
Total units/day = 15 + 12 + 10 = 37​
→ B’s share = (12 / 37) × 5550 = ₹1800

✅ Final Answer: ₹1800

If 4 men and 6 boys can do a work in 8 days and 6 men and 4 boys can do the same work
in 7 days, then how many days will 5 men and 4 boys take to do the same work?

🟩 1st line:
Asha and Bhuvan can do a piece of work in 6 days and 9 days, respectively.​
→ Asha’s 1 day work = 1/6​
→ Bhuvan’s 1 day work = 1/9

🟩 2nd line:
They work on alternate days, starting with Asha.​
Let’s calculate alternate day-wise total work:

●​ Day 1 (Asha): +1/6

●​ Day 2 (Bhuvan): +1/9
●​ Day 3 (Asha): +1/6
●​ Day 4 (Bhuvan): +1/9
●​ Day 5 (Asha): +1/6
●​ Day 6 (Bhuvan): +1/9
●​ Day 7 (Asha): ?

Ab in 6 days ka kaam add karte hain:

→ (1/6 + 1/9) × 3 =​
→ LCM = 18 → (3/18 + 2/18) = 5/18 per 2 days​
→ 3 cycles = (5/18 × 3) = 15/18 work done in 6 days

🟩 3rd line:
Remaining work = 1 - 15/18 = 3/18 = 1/6​
→ Day 7: Asha’s turn → Asha does 1/6 work per day​
→ 1/6 work completed → Done on Day 7
✅ Final Answer: 7 days

💡 Cycle ka matlab kya hota hai yahaan?

Ek cycle = Asha ka ek din + Bhuvan ka ek din​
= 2 din ka combo (Asha + Bhuvan)

🔁 Cycle use karne ka fayda kya hai?

Agar alternate din kaam ho raha hai, toh:

●​ 2 din mein ek pattern repeat hota hai (Asha then Bhuvan).

●​ Isliye, 2 din ko ek group ya “cycle” treat kar lete hain.
●​ Fir aap dekh sakte ho ki kitne aise 2-2 din wale cycles total mein ho rahe hain.

🧠 Example se samjho:
Asha 1 din mein karta hai = 1/6​
Bhuvan 1 din mein karta hai = 1/9

Toh 2 din mein milke karte hain =​

1/6 + 1/9 = 5/18 (yeh ek cycle ka kaam ho gaya)

✅ Ab dekhte hain 6 din tak kitne cycles hue?

●​ Day 1–2 → Asha + Bhuvan = 1 cycle
●​ Day 3–4 → Asha + Bhuvan = 2nd cycle
●​ Day 5–6 → Asha + Bhuvan = 3rd cycle

Toh 3 cycles = 6 din

Aur har cycle mein 5/18 work hota hai​

→ Total 3 cycles = 15/18 kaam

🧮 Bacha hua kaam = 1 - 15/18 = 3/18 = 1/6

●​
✅
Day 7: Asha ka turn — aur Asha 1 din mein 1/6 kaam karta hai​
→ Toh Day 7 pe pura kaam finish
 🔚 Final samjho: Days Worker Work done

Day 1 Asha 1/6

Day 2 Bhuvan 1/9

Day 3 Asha 1/6

Day 4 Bhuvan 1/9

Day 5 Asha 1/6

Day 6 Bhuvan 1/9

Day 7 Asha 1/6 (remaining)

✅ Answer: Total 7 days

Agar ab bhi koi part confuse kar raha ho, toh woh specific line batao — usko aur zyada easy bana ke samjha dungi.

20 workers can paint 24 walls in 36 days. In how many days can 30 workers paint 20
walls?

✅ 1st line:
"20 workers can paint 24 walls in 36 days."​
→ Total work = 20 workers × 36 days = 720 worker-days​
This paints 24 walls,​
So, to paint 1 wall, work needed = 720 ÷ 24 = 30 worker-days

✅ 2nd line:
"In how many days can 30 workers paint 20 walls?"​
→ Total work = 30 worker-days × ? days = 30 × D​
But 1 wall needs 30 worker-days​
So, 20 walls need = 30 × 20 = 600 worker-days

Now use:​
30 workers × D = 600​
⇒ D = 600 ÷ 30 = 20 days
✅ Final Answer:
30 workers will take 20 days to paint 20 walls. ✅
A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can
do the same work in 56 days. They started working together and completed the work
such that B did not work on last 2 days and A did not work on the last 3 days. In how
many days (total) was the work completed?

✅ 1st line:
A alone can do a work in 14 days.​
→ A's 1 day work = 1/14

✅ 2nd line:
B alone can do the same work in 28 days.​
→ B's 1 day work = 1/28

✅ 3rd line:
C alone can do the same work in 56 days.​
→ C's 1 day work = 1/56

✅ 4th line:
They started working together and completed the work such that B did not work on last 2
days​
→ This means:​
Let total work complete in D days​
So, B worked for (D − 2) days

✅ 5th line:
A did not work on the last 3 days​
→ So, A worked for (D − 3) days​
C worked all D days
✅ 6th line:
Now total work = 1 (full work)

Total work done =​

= A’s contribution + B’s contribution + C’s contribution​
= (D − 3) × (1/14) + (D − 2) × (1/28) + D × (1/56)

Now, take LCM of 14, 28, 56 = 56​

→ Convert each:

●​ (D − 3) × 4/56
●​ (D − 2) × 2/56
●​ D × 1/56

So total:​
= [4(D − 3) + 2(D − 2) + D] / 56 = 1

→ 4D − 12 + 2D − 4 + D = 56​
→ (4D + 2D + D) − (12 + 4) = 56​
→ 7D − 16 = 56​
→ 7D = 72​
→ D = 10.29 days

✅ Final Answer:
Total days = approx 10.29 days (or 10 days + 1/4 day) ✅
A alone can do a work in 11 days. B alone can do the same work in 22 days. C alone can
do the same work in 33 days. They work in the following manner.

Day1: A and B work.

Day2: B and C work.

Day3: C and A work.

Day4: A and B work. And so on.

In how many days will the work be completed?

✅ 1st line:
A alone can do a work in 11 days.​
→ A’s 1-day work = 1/11

✅ 2nd line:
B alone can do the same work in 22 days.​
→ B’s 1-day work = 1/22

✅ 3rd line:
C alone can do the same work in 33 days.​
→ C’s 1-day work = 1/33

✅ Cycle pattern given:

They repeat this every 3 days.

●​ Day 1: A + B​
→ Work = 1/11 + 1/22 = (2 + 1)/22 = 3/22​

●​ Day 2: B + C​
→ Work = 1/22 + 1/33​
→ LCM = 66​
→ Work = (3 + 2)/66 = 5/66​

●​ Day 3: C + A​
→ Work = 1/33 + 1/11 = (1 + 3)/33 = 4/33​

✅ Work in 3-day cycle:

●​ Day 1: 3/22
●​ Day 2: 5/66
●​ Day 3: 4/33

Convert all to same denominator (LCM = 66):

●​ 3/22 = 9/66
 ●​ 5/66 = 5/66
●​ 4/33 = 8/66

Total in 3 days = 9 + 5 + 8 = 22/66 = 1/3

✅ Total work = 1
✅
So in 3 days, 1/3 work is done​
→ In 9 days, 3 × 1/3 = full work completed

✅ Final Answer:
Work completed in 9 days ✅
24 - 6 - 2025
A and B can do a piece of work in 25 days.​
B alone can do 66 2/3 % of the same work in 30 days.In how many days can A alone do
4/15 part of the same work?

✅ 1st line:
A and B can do the work together in 25 days​
→ A + B's 1-day work = 1/25

✅ 2nd line:
👉
B alone can do 66 2/3 % of the work in 30 days​
66 2/3% = 2/3 of work

→ Time to do 2/3 work = 30 days​

→ So, B's full work time = 30 ÷ (2/3) = 45 days​
→ So, B's 1-day work = 1/45

💡 Find A’s 1-day work:

We know:​
A + B = 1/25​
B = 1/45​
So,

A = (1/25 - 1/45)
= (9 - 5) / 225
= 4 / 225

→ A's 1-day work = 4/225

✅ 3rd line:
We have to find in how many days A can do 4/15 of the work.

We know:​
A's 1-day work = 4/225​
Let days = x​
Then,

x × (4/225) = 4/15
→ x = (4/15) ÷ (4/225)
→ x = (4/15) × (225/4)
→ x = 225 / 15 = 15

✅ Final Answer: 15 days ✅

Avi and Bindu can complete a project in four and twelve hours. respectively. Avi begins
project at 5a.m., and they work alter-nately for one hour each. When will the project be
completed?

✅ 1st line:
Avi and Bindu can complete a project in 4 and 12 hours respectively.​
→ Avi's 1-hour work = 1/4​
→ Bindu's 1-hour work = 1/12

✅ 2nd line:
Avi begins at 5 a.m., and they work alternately for 1 hour each.

→ Work pattern:

●​ 5–6 a.m. → Avi → 1/4

●​ 6–7 a.m. → Bindu → 1/12
●​ 7–8 a.m. → Avi → 1/4
●​ 8–9 a.m. → Bindu → 1/12
●​ … (repeats)

In 2 hours (1 cycle), work done = 1/4 + 1/12 = (3+1)/12 = 4/12 = 1/3

✅ 3rd line:
When will the project be completed?

→ After 2 hours → 1/3 done​

→ After 4 hours → 2/3 done​
→ After 6 hours → full work done

So, project completes in 6 hours

✅ Final Answer:
✅
📌
5 a.m. + 6 hours = 11 a.m. ​
Project completes at 11 a.m.

A can do a piece of work in 24 days and B can do it in 80 days. B works alone for 2 days
and A works alone on the 3rd day. This process continues till the work is completed. In
how many days will the work be completed?

Let’s solve this step-by-step — line by line and in simple words:

✅ 1st line:
A can do a piece of work in 24 days, B in 80 days

●​ A's 1-day work = 1/24

●​ B's 1-day work = 1/80

✅ 2nd line:
B works alone for 2 days

→ B's 2-day work = 2 × 1/80 = 2/80 = 1/40

✅ 3rd line:
A works alone on the 3rd day
→ A's 1-day work = 1/24

✅ 4th line:
This 3-day cycle continues: 2 days B + 1 day A

→ Work in 3 days = 1/40 (B's 2 days) + 1/24 (A's 1 day)​

→ LCM of 40 and 24 = 120​
→ Work = (3 + 5)/120 = 8/120 = 1/15

So, 1/15 work done in 3 days

✅ 5th line:
How many days to complete?

→ In 3 days ⇒ 1/15 work​

→ Full work ⇒ 15 × 3 = 45 days

✅ ✅ Final Answer:
📌 Total time to complete the work = 45 days ✅
If, in a family, consumption of sugar is 6 kg for 24 days, then what is the consumption of
sug-ar for 18 days?

✅ 1st line:
➡️
If, in a family, consumption of sugar is 6 kg for 24 days​

➡️
This means in 24 days, sugar used = 6 kg​
So, 1 day’s consumption = 6 ÷ 24 = 0.25 kg/day

✅ 2nd line:
➡️
What is the consumption of sugar for 18 days?​

➡️
1 day = 0.25 kg​
So, 18 days = 0.25 × 18 = 4.5 kg
✅ Final Answer:
📌 Sugar consumption for 18 days = 4.5 kg ✅
16 men can paint 15 walls in 45 days. In how many days can 20 men paint 20 walls?

✅ 1st line:
➡️
"16 men can paint 15 walls in 45 days"​

➡️
Total work = 16 men × 45 days = 720 man-days​

➡️
This work = 15 walls​
So, work per wall = 720 ÷ 15 = 48 man-days per wall

✅ 2nd line:
➡️
"In how many days can 20 men paint 20 walls?"​

➡️
Total work = 20 walls × 48 man-days = 960 man-days​
20 men working daily ⇒ Days = 960 ÷ 20 = 48 days

✅ Final Answer:
📌 20 men can paint 20 walls in 48 days ✅
If Mona and Sona together can finish a typing work in 18 days and Sona alone can finish
it in 24 days, find the number of days in which Mona alone can finish the work.

✅ 1st line:
➡️
"Mona and Sona together can finish a typing work in 18 days"​
Together’s 1 day work = 1/18

✅ 2nd line:
➡️
"Sona alone can finish it in 24 days"​
Sona’s 1 day work = 1/24
✅ 3rd line:
➡️
"Find the number of days in which Mona alone can finish the work"​
Mona’s 1 day work = Together – Sona = 1/18 – 1/24

Take LCM of 18 and 24 = 72​

So,​
1/18 = 4/72​
1/24 = 3/72​
Then,​
Mona’s 1 day work = 4/72 – 3/72 = 1/72​
➡️ So, Mona alone can do the work in 72 days

✅ Final Answer:
📌 Mona alone can finish the work in 72 days ✅
A man takes 16 days to com-plete a project. A woman does the same work in 12 days.
They started the work together on al-ternate days and the man worked on the first day.
How much time will they take to com-plete the work?

A can do a piece of work in 15 days, but with the help of B, he can do it 9 days. In what
time can B do it alone?

✅ 1st line:
➡️
"A can do a piece of work in 15 days"​
A’s 1 day work = 1/15

✅ 2nd line:
➡️
"With the help of B, A can do it in 9 days"​
A + B's 1 day work = 1/9

✅ 3rd line:
"In what time can B do it alone?"​
B’s 1 day work = (A + B)'s work – A's work​
= 1/9 – 1/15​
LCM of 9 and 15 = 45​
= 5/45 – 3/45 = 2/45

➡️ B alone can do the work in 45/2 = 22.5 days

✅ Final Answer:
📌 B alone can do the work in 22.5 days (or 22 days 12 hours) ✅
A can do a piece of work alone in 96 days and B can do it alone in 104 days. In how many
days can the duo, working together, complete the work?

Let’s solve line by line, clearly and with fewer words:

✅ 1st line:
➡️
"A can do a piece of work alone in 96 days"​
A’s 1-day work = 1/96

✅ 2nd line:
➡️
"B can do it alone in 104 days"​
B’s 1-day work = 1/104

✅ 3rd line:
"In how many days can the duo, working together, complete the work?"
✅ Final Answer:
📌 A and B together can complete the work in approx. 49.92 days (or 49 days 22 hours)
Asha and Bhuvan can do a piece of work in 6 days and 9 days, respectively. They work
on al-ternate days, starting with Asha on the first day. In how many days will the work be
complet-ed?

✅ 1st line:
"Asha and Bhuvan can do a piece of work in 6 days and 9 days, respectively."

●​ Asha's 1-day work = 1/6

●​ Bhuvan's 1-day work = 1/9

✅ 2nd line:
"They work on alternate days, starting with Asha on the first day."

●​ Odd days: Asha works → 1/6 work

●​ Even days: Bhuvan works → 1/9 work
●​ So, work done in 2 days = 1/6 + 1/9 = (3 + 2)/18 = 5/18

✅ 3rd line:
"In how many days will the work be completed?"

Let’s keep adding 2-day work blocks until total work reaches 1:

●​ After 2 days → 5/18 done

●​ After 4 days → 5/18 × 2 = 10/18 = 5/9
●​ After 6 days → 5/18 × 3 = 15/18 = 5/6

After 6 days, 5/6 of the work is done.​

Remaining work = 1 – 5/6 = 1/6

7th day: Asha’s turn again. She does 1/6 work in a day.​
So, she finishes the remaining work on the 7th day.

✅ Final Answer:
📌 The work will be completed in 7 days. ✅
If 5 persons can prepare 5 ta-bles in 5 day, then how long will it take 25 persons to
prepare 25 tables?

Let’s solve it step-by-step and line-by-line:

✅ 1st line:
"If 5 persons can prepare 5 tables in 5 days,"

👉 This means:
●​ 5 persons → 5 tables → in 5 days

So,

●​ 1 person can prepare 1 table in 5 days

✅ 2nd line:
"Then how long will it take 25 persons to prepare 25 tables?"

We already know:
 ●​ 1 person takes 5 days for 1 table

Now,

●​ 25 persons can make 25 tables in the same 5 days,​

because each person makes 1 table in 5 days.

✅ Final Answer:
📌 5 days ✅
Arun alone can finish a work in 12 days and Shama alone can do it in 15 days. How much
time will be taken to finish the work, if Arun and Shama work togeth-er?

Let’s solve it line by line in clear and short steps:

✅ 1st line:
"Arun alone can finish a work in 12 days and Shama alone can do it in 15 days."

●​ Arun's 1 day work = 1/12

●​ Shama's 1 day work = 1/15

✅ 2nd line:
"How much time will be taken to finish the work,"
A is 3 times as fast as B and is, therefore, able to complete a work in 32 days lesser than
B. A and B, working together, can complete the work in

➡️
1st line: A is 3 times as fast as B​
That means:​
If B takes x days,​
Then A takes x ÷ 3 = x/3 days.

➡️
2nd line: A completes the work in 32 days less than B​
A’s time = B’s time − 32​
So:​
x − x/3 = 32​
⇒ (3x − x)/3 = 32​
⇒ 2x/3 = 32​
⇒ x = 48 days (B’s time)

So A’s time = x/3 = 48/3 = 16 days

3rd line: A and B together can complete the work in ?

➡️ A’s 1 day work = 1/16​
➡️ B’s 1 day work = 1/48​
Together = 1/16 + 1/48​
LCM of 16 and 48 = 48​
⇒ (3 + 1)/48 = 4/48 = 1/12

So, together they complete the work in 12 days. ✅

Final Answer: 12 days