Time and work

Formulae
1. If A can do a piece of work in n days,
then A’s 1 day work = 1/n
2. If A’s 1 day work = 1/n,
Then A can finish the work in n days.
3. The ratio of work done by A and B = 3 : 1, then
The ratio of time taken by A and B to complete the
work = 1 : 3

I. Answer the following :

Type -I
1. If Roger can do a piece of work in 8 days and Antony can
complete the same work in 5 days, In how many days will
both of them together complete it.

3 13 = 4 days
1
Ans:

2. A can do a job in 12 days and B can do the same job in

16 days. How long will it take for both A and B to complete the job

if they work together?

Ans: 7 days
Soln:
A’s 1 day work= 1/12
 B’s 1 day work = 1/16
(A + B)’s 1 day work = 1/12 +1/16= 7/48
(A+B) can finish the job in 48/7 = 6.87 = 7 days

Type – II

3. If A and B together can complete a piece of work in 15

days and B alone in 20 days. In how many days can A

alone complete the work? Ans:60 days

Soln: A+B -----1/15

B ------ 1/20

A+B – C ------- 1/15 -1/20

4. A can do a certain work in the same time in which B and

Ctogether can do it . If Aand Btogether could do it in 10

 d ay s an d C alo n e in 50d ay s,th en B alo n e co u ld d o it in

h o w m an y d ay s? (sy n erg y )

Soln: a = b+c

(a+b)’s 1 day work = 1/10

c’s 1 day work =1/50

(a+b+c)’s 1 day work = 1/10 +1/50 = 6/50

(a+b+c) = 6/50

(a +a) = 6/50

2a =6/50

a=3/50

b =(a+b)-a = 1/10 – 3/50 = 1/25

Ans:25 days
 5. Acan do a piece of work in 4 hours, Band Ctogether can

do it in 3 hours, while Aand Ctogether an do it in 2

hours.

Howlong Balone will take to do it? (synergy) Ans: 12 hrs

Solution:

A’s 1 hr work = ¼ , (B+C)’s 1 hr work = 1/3 , (A+C)’s 1 hr work=

1/2

C’s 1 hr work = ( A+C) –A=½- ¼=¼

B’s 1 hr work = (B+C)- C = 1/3 – ¼ =1/12

B can complete the work in 12days

Type - 3
 6. If 6 men and 8 boys can do a piece of work in 10 days

hile 26 men and 48 boys can do the same in 2 days,

W

what is the time taken by 15 men and 20 boys in doing

the same type of work? (synergy) Ans: 4 days

Soln: 6 men and 8 boys can do a piece of work in 10 days

26 men and 48 boys can do the same in 2 days

Calculation

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

⇒ M = 2B

⇒ B = M/2 ----(1)

Now substitute (1) in 15M + 20B

⇒ 15M + 10M = 25M

Now, 6M + 8B in 10 days

⇒ (6M + 4M) 10 = 100M

Then D(25M) = 100M

⇒ D = 4 days.

∴ The time taken by 15 men and 20 boys to do the same type of work
will be 4 days.
7. 4 men and 6women can complete a work in 8 days, while

3men and 7women can complete it in10 days. In how

many days will 10 women complete it ?Ans: 40 days

Let 1 man's 1 day's work =x

1 woman's 1 day's work =y.
Then, 4x+6y=1/8
3x+7y=1/10.
Solving the two equations,
x=11/400,y=1/400
∴ 1 woman's 1 day's work =1/400.
⇒ 10 women's 1 day's work =(1/400×10)=1/40.
Hence, 10 women will complete the work in 40 days.

8. If 2 m en an d 3b o y s can d o a p iece o f w o rk in 10 d ay s,

while 3 men and 2 boys can do the same work in 8 days.

 In h o w m an y d ay s can b o y s can 2 m en an d 1 b o y d o th e

:12 2 days
1
work? Ans

Solution:

1 man’s 1 day work =x,

1 boy’s 1 day work = y

2x + 3y = 1/10

3x + 2y = 1/8

Solving for x & y

x=7/200 , y= 1/100

2 men + 1 boys 1 day work = 2x7/200 + 1x 1/100

=16/200 = 2/25

So, 2 men and 1 boy can finish the work in 25/2 = 12 ½ days

Type – 4
9. A contractor undertakes to do a job in 40 days. He

em p lo y ed 100 m en at th e b eg in n in g an d 100 m o re after

35 d ay s, an d co m p letes th e w o rk in stip u lated tim e, If h e

h ad n o t en g ag ed th e ad d itio n al m en . H o w m an y d ay s

b eh in d sch ed u led w o u ld it b e fin ish ed ? A n s: 5 d ay s

Soln: work = men x days

=100x35 + 200x5

=3500 + 1000

W=4500 units

If he had not engage additional man, then

Work = men x days

4500 = 100 x days

Days = 4500/100 =45 days

Additional days = 45- 40 = 5 days

10. A C o n tracto r em p lo y ed 30m en to d o a p iece o f w o rk

in 38 d ay s. A fter 25 d ay s, h e em p lo y ed 5 m en m o re an d
the work was finished one day earlier. How many days he

would be behind, if he had not employed additional men

A n s: 39 d ay s

Solution: 30m------ 38 days

A fter 25 d ay s-- +5m (30+5=35men)

Now35 m----- 38- 25=13 days

They complete the work1 day earlier

So, (13 -1)= 12 days

Now, 35 men ----12 days x= 35 x 12

30 men --- ? days 30

=14 days

25 + 14 = 39days
Type - 5

11. “A” can do a piece of work in 16 days and Bcan do

th e sam e w o rk in 12 d ay s. T h ey w o rk to g eth er fo r 3 d ay s

an d th en “A ” leav es. In h o w m an y m o re d ay s w ill B

co m p lete th e rem ain in g w o rk ? A n s:6 4 = 7d ay s

3

12. A can d o a w o rk in 10 d ay s an d B can d o th e sam e w o rk

in 15 d ay s. T h ey w o rk to g eth er fo r 4 d ay s an d th en B

leav es. In h o w m an y m o re d ay s w ill A co m p lete th e

rem ain in g w o rk ? A n s :4d ay s

13. A can d o a w o rk in 36 d ay s an d B can d o th e sam e

w o rk in 54 d ay s. T h ey w o rk to g eth er fo r 12 d ay s an d th en

A leav es. In h o w m an y m o re d ay s w ill B co m p lete th e

rem ain in g w o rk ? A n s :24 d ay s

Solution: A’s 1 day work = 1/36

B’s 1 day work = 1/54

(A + B )’s 1 d ay w o rk = 1/36 + 1/54 = 5/108

(A + B )’s 12 d ay w o rk = 12 x 5/108 = 5/9

Remaining work = 1- 5/9 = 4/9

B can co m p lete th e rem ain in g w o rk in 54 d ay s = 4/9 x 54

 = 24

days

Type – 6

14. Kamal can do a work in 15 days. Vimal is 50% more

efficient than Kamal. How many days Vimal will take to

do the same piece of work? Ans : 10 days

15. A d o es 20% less w o rk th an B . If A co m p letes a

72 h rs. T h en B can d o it in ? A n s : 6
1
piece of work in

h rs
 16. A is 30% m o re efficien t th an B . H o w m u ch tim e

w ill th ey w o rk in g to g eth er, tak e to co m p lete a jo b w h ich

A alo n e co u ld h av e d o n e in 23 d ay s? A n s:13 d ay s
Solution: A B

13 10 30% = 30/100 = 3/10

A = 10+3 = 13

A + B can do the job in 13 + 10 =23 days

Therefore” A” can do in (13 x 23)/23 =13days

2 nd method

Ratio of times taken by A and B =100:130=10:13.

Suppose B takes x days to do the work.
Then, 10:13::23:x ⇒ x=(23×1310)⇒x=29910.
A's 1 day's work =123;
B's 1 day's work =10299;
(A+B)'s 1 day's work =(123+10299)=23299=113
Therefore, A and B together can complete the work in 13 days.