PERCENTAGE:

1.
A shopkeeper increases the price of a product by 25% and then o ers a discount of 20% on the
marked price. What is the overall percentage change in the price paid by the customer compared to
the original price?

2.
A's salary is 40% more than B's salary, and B’s salary is 25% more than C’s salary. By what percentage
is A’s salary more than C’s salary?

3.
In an elec on, Candidate A got 55% of the total valid votes, while Candidate B got the remaining. If
10% of the total votes were invalid and the total number of votes was 80,000, how many more valid
votes did Candidate A get than Candidate B?

4.
A student got 60% marks in 5 subjects together. The maximum marks per subject were 100. If he
scored 75% in the rst subject, 80% in the second, 40% in the third, and 50% in the fourth, what is
the percentage of marks he must score in the h subject to maintain the overall percentage?

5.
A man spends 80% of his income. His income increases by 25%, and his expenditure increases by
20%. Find the percentage increase in his savings.

6.
A dealer marks his goods 40% above the cost price and allows a discount of 10% to customers. If the
customer s ll pays ₹270 more than the cost price, what was the cost price of the ar cle?

7.
In a class, 40% of the students passed in English, 50% passed in Maths, and 20% passed in both. If
there are 200 students, how many failed in both subjects?

8.
An alloy contains copper and zinc in the ra o 7:3. How much percentage of copper must be added to
100 kg of the alloy so that the new mixture has 80% copper?
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 9.
A popula on of a town increased by 20% in the rst year and decreased by 10% in the second year.
What is the net percentage change in the popula on over the two years?

10.
A machine depreciates at a rate of 20% per annum. What will be its value a er 3 years if the current
value is ₹1,00,000?

11.
An item was bought at a discount of 20% on the marked price. The item was sold at a pro t of 25%
on the price it was bought. What was the overall percentage gain on the marked price?

12.
The price of petrol increased by 25%. By what percentage should a person reduce his consump on
so that his expenditure remains the same?

13.
The income of A is 20% less than that of B, and the income of C is 25% more than that of B. By what
percentage is C’s income more than A’s?

14.
A wholesaler allows a discount of 10% to a retailer, who further allows a discount of 5% to a
customer. If the customer pays ₹513 for a product, what was the original marked price?

15.
The value of a machine depreciates by 10% in the rst year, 15% in the second year, and 20% in the
third year. What will be the value of the machine a er 3 years if its original value was ₹50,000?

RATIO AND PROPORTION:

1.
The incomes of A, B, and C are in the ra o 4:5:6 and their expenditures are in the ra o 6:5:4. If A
saves ₹5,000, B saves ₹10,000, nd the income of C.

2.
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 A container has a mixture of milk and water in the ra o 7:5. If 6 liters of mixture is taken out and
replaced with water, the ra o becomes 1:1. Find the original quan ty of the mixture.

3.
Two alloys A and B are made up of gold and copper in the ra o 5:3 and 7:5 respec vely. If 30 grams
of alloy A is mixed with 20 grams of alloy B, what is the ra o of gold to copper in the new alloy?

4.
A sum of ₹65,000 is divided among A, B, and C such that A:B = 2:3 and B:C = 4:5. Find the share of
each.

5.
A bag contains black, white, and red balls in the ra o 4:5:6. If there are 15 more red balls than black
balls, nd the total number of balls.

6.
The ra o of the number of boys to girls in a school is 3:4. If 20 boys leave and 40 girls join, the ra o
becomes 2:3. Find the original number of boys and girls.

7.
A mixture of two liquids A and B is in the ra o 3:2. When 10 liters of mixture is replaced with liquid B,
the ra o becomes 1:1. Find the original quan ty of the mixture.

8.
Three partners A, B, and C invest in a business in the ra o 5:6:8. A er 4 months, A withdrew half his
capital, and B doubled his. At the end of the year, they made a pro t of ₹78,000. What is C’s share of
the pro t?

9.
A man divided his property among his three children in the ra o 3:4:6. If the di erence between the
largest and the smallest shares is ₹3,00,000, nd the total value of the property.

10.
A and B can do a piece of work in the ra o 5:3. If A alone can complete the work in 20 days, in how
many days can they together complete the work?
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 11.
Two vessels contain mixtures of milk and water in the ra o 7:3 and 5:3 respec vely. In what ra o
should the contents of the two vessels be mixed to obtain a mixture containing milk and water in the
ra o 3:1?

12.
A, B, and C receive pro ts in a business in the ra o 5:3:2. If A receives ₹20,000 more than C, nd the
total pro t.

13.
A sum of money is divided among A, B, C, and D in the ra o 2:3:5:7. If D gets ₹630, nd the total sum
and each person’s share.

14.
If 3A = 4B and 5B = 6C, nd the ra o A:B:C.

15.
Two numbers are in the ra o 5:7. If 8 is added to each, the new ra o becomes 3:4. Find the original
numbers.

AVERAGES:
1.
The average age of a class of 40 students is 18 years. When 10 new students joined, the average age
increased by 0.5 years. What is the average age of the 10 new students?

2.
The average of ve numbers is 54. If one number is excluded, the average becomes 50. What is the
excluded number?

3.
A batsman has an average score of 48 in 25 innings. If his highest and lowest scores are removed, the
average of the remaining 23 innings becomes 47. Find the di erence between his highest and lowest
scores.

4.
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The average weight of A, B, and C is 60 kg. The average weight of A and B is 65 kg, and the average
weight of B and C is 55 kg. Find the weight of B.

5.
The average marks of a class of 80 students in an exam is 72. The average marks of the top 20
students is 90 and that of the bo om 30 is 60. Find the average marks of the remaining 30 students.

6.
The average of 10 numbers is 45. If the average of the rst 4 numbers is 42 and the average of the
next 4 is 48, what is the average of the last 2 numbers?

7.
The average temperature of a city from Monday to Saturday is 28°C, and the average from Tuesday
to Sunday is 30°C. If the temperature on Monday was 25°C, what was the temperature on Sunday?

8.
The average salary of 40 employees in an o ce is ₹52,000. If the average salary of 30 employees is
₹50,000 and that of the remaining is ₹58,000, verify the overall average.

9.
The average weight of 6 persons increases by 1.5 kg when one new person joins. If the weight of the
new person is 75 kg, what was the average weight before he joined?

10.
The average age of a family of 5 members is 30 years. A baby is born, and now the average age
becomes 26. What is the age of the baby?

11.
In a group of 10 students, the average marks in mathema cs are 70. Later it was found that one
score was wrongly recorded as 82 instead of 62. Find the correct average.

12.
The average of three numbers is 40. If the rst number is 4 more than the second, and the second is
8 more than the third, nd the numbers.
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 13.
The average of 25 numbers is 36. The average of the rst 13 numbers is 32, and the average of the
last 13 numbers is 40. Find the 13th number (common to both halves).

14.
A cricketer played 10 matches and scored an average of 50 runs. In the next 5 matches, he scored an
average of 60 runs. What is his new average a er 15 matches?

15.
A student scored an average of 65 marks in 6 subjects. If the marks in 5 subjects were 70, 62, 58, 74,
and 68, nd the marks scored in the sixth subject.

PROFIT, LOSS AND DISCOUNT:

1.
A shopkeeper marks an ar cle 40% above the cost price and allows a discount of 20%. If he s ll
makes a pro t of ₹480, nd the cost price of the ar cle.

2.
A man sells two ar cles at ₹1,200 each. On one he gains 20% and on the other he loses 20%. Find
the overall pro t or loss percentage.

3.
A trader sold an ar cle at a loss of 10%. Had he sold it for ₹80 more, he would have gained 5%.
Find the cost price of the ar cle.

4.
A manufacturer sells an ar cle to a wholesaler at 20% pro t, the wholesaler sells it to a retailer at
25% pro t, and the retailer nally sells it to a customer at a loss of 10%. If the customer pays ₹990,
nd the cost price for the manufacturer.

5.
A dealer marks an item 50% above cost price. He gives successive discounts of 10% and 20% and
s ll makes a pro t of ₹120. What is the cost price?

6.
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 By selling 25 pens for ₹480, a man incurs a loss equal to the cost price of 5 pens. Find the cost price
of one pen.

7.
A retailer bought 50 kg of rice at ₹40/kg and 30 kg at ₹60/kg. He mixed both and sold the mixture
at ₹55/kg. Find his total pro t or loss percentage.

8.
An ar cle is sold at a discount of 20% on its marked price. Even then, the seller makes a pro t of
25%. Find the markup percentage on the cost price.

9.
A vendor gains 20% by selling a product at a discount of 10% on the marked price. Find the pro t
percentage if no discount had been o ered.

10.
A man buys 2 bicycles for ₹2,000. He sells one at a pro t of 20% and the other at a loss of 10%. If
he breaks even overall, nd the cost price of each bicycle.

11.
A person sells an ar cle at 15% loss. If he had sold it for ₹120 more, he would have gained 10%.
Find the cost price.

12.
A dealer sells his goods at a 30% pro t a er allowing a discount of 10% on the marked price. If the
cost price is ₹630, nd the marked price.

13.
A merchant gains 10% on selling an ar cle at a discount of 5%. Find the ra o of the cost price to
the marked price.

14.
A watch is sold at a pro t of 15%. If it had been sold for ₹50 more, the pro t would have been
25%. Find the cost price.
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 15.
A product passes through three hands before reaching the consumer. Each earns a pro t of 20% on
the cost to them. If the consumer pays ₹1,728, what was the original cost price?

TIME, SPEED AND DISTANCE:

1.
A train covers a certain distance at a speed of 60 km/h and returns at a speed of 90 km/h. Find the
average speed for the en re journey.

2.
Two trains, 150 meters and 200 meters long respec vely, are running in opposite direc ons on
parallel tracks at speeds of 60 km/h and 90 km/h. How long will it take for them to completely
cross each other?

3.
A man walks at 5 km/h and reaches his o ce 10 minutes late. If he walks at 6 km/h, he reaches 5
minutes early. Find the distance between his home and o ce.

4.
A car covers a distance of 240 km at three di erent speeds: 60 km/h for the rst part, 80 km/h for
the second, and 100 km/h for the last. If the three parts are equal in distance, nd the average
speed for the en re journey.

5.
A train takes 30 seconds to cross a man walking at 6 km/h in the same direc on. It takes 20
seconds to cross the same man walking in the opposite direc on. Find the length and speed of the
train.

6.
Two ci es A and B are 360 km apart. A car starts from A towards B at 60 km/h, and at the same
me another car starts from B towards A at 40 km/h. When will they meet and how far from A?

7.
A cyclist covers a certain distance in 5 hours. If his speed had been 4 km/h more, he would have
taken one hour less. Find the distance.
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 8.
A train crosses a pla orm 200 meters long in 36 seconds and a man standing on the pla orm in 18
seconds. Find the speed of the train and the length of the train.

9.
A person travels from A to B at 45 km/h and returns at 75 km/h. If the total me taken is 8 hours,
nd the distance between A and B.

10.
A boat takes 6 hours to travel downstream from point A to B and 9 hours to return. If the speed of
the boat in s ll water is 20 km/h, nd the speed of the stream and the distance between A and B.

11.
A train 240 m long takes 30 seconds to cross a bridge and 18 seconds to cross a man running at 6
km/h in the direc on of the train. Find the length of the bridge and the speed of the train.

12.
A car covers half the distance at 60 km/h and the other half at 90 km/h. What is the average speed
for the en re journey?

13.
A person takes 3 hours to travel a certain distance by car. If he increases his speed by 20 km/h, he
takes 30 minutes less. Find the original speed and distance.

14.
Two trains leave sta ons A and B towards each other at speeds of 72 km/h and 54 km/h
respec vely. If the distance between the sta ons is 378 km, a er how long will they meet?

15.
A man walks from his house to a sta on at 5 km/h and catches a train that reaches his o ce at
9:00 a.m. If he had walked at 7 km/h, he would have caught a train that arrives at 8:40 a.m. What
is the distance between his house and the sta on?

SIMPLE INTEREST AND COMPOUND INTEREST:

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 1.
A sum amounts to ₹6,600 in 2 years and ₹7,590 in 4 years at simple interest. Find the rate of
interest and the principal.

2.
The di erence between the compound interest and simple interest on a sum of ₹12,000 for 2 years
at 10% per annum is ₹120. Find the compound interest.

3.
A certain sum becomes ₹7,744 in 2 years and ₹9,025.60 in 3 years at compound interest
compounded annually. Find the rate of interest and the principal.

4.
At what rate percent per annum will a sum of ₹10,000 amount to ₹12,100 in 2 years compounded
annually?

5.
A person invests ₹8,000 at 10% p.a. compounded half-yearly. Find the amount and compound
interest a er 1.5 years.

6.
A sum of ₹25,000 was invested in two parts — one at 10% simple interest and the other at 8%
compound interest. A er 2 years, the total interest received was ₹4,320. Find the amount invested
in each part.

7.
What sum of money will amount to ₹19,360 in 3 years at 20% p.a. compound interest,
compounded annually?

8.
The di erence between compound interest and simple interest on a certain sum for 2 years at 5%
per annum is ₹30. Find the sum.

9.
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 A certain amount doubles itself in 5 years at compound interest compounded annually. In how
many years will it become eight mes itself?

10.
A sum of ₹15,000 is invested at compound interest, compounded annually. It becomes ₹18,150 in 2
years. Find the rate of interest per annum.

11.
A person borrowed ₹16,000 for 3 years. He paid ₹1,800 as simple interest. Find the rate of interest
per annum.

12.
At what rate of compound interest will a sum of ₹20,000 become ₹24,200 in 2 years?

13.
If the compound interest on a sum for 2 years at 4% p.a. is ₹816, nd the principal.

14.
A man lent ₹12,000 partly at 10% and partly at 12% simple interest per annum. If the annual
interest is ₹1,280, nd the amount lent at each rate.

15.
A sum of ₹40,000 is invested at compound interest at 5% p.a. for 3 years. What will be the
di erence between the compound interest and simple interest for the same period?
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