CBSE Class 10 Mathematics Percentage MCQs Set 28

Mathematics Objective Questions and Answers: Percentage

Review structured MCQ sets for Class 10 Mathematics Percentage. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Download Percentage MCQs with Answers

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Multiple Choice Questions

Question 1: Madan spends 50% of his income on household expenditure and 60% of the remaining on personal expenditure. Of the remaining, he pays 50% towards income tax and saves the remaining Rs. 1200. What is his personal expenditure?
(a) Rs. 1800
(b) Rs. 2400
(c) Rs. 3600
(d) Rs. 4800
Show Answer & Explanation

Answer: (c) Rs. 3600

Explanation:
1. Let the income be 100: household 50, remaining 50
2. Personal = 60% of 50 = 30, remaining 20
3. Tax = 50% of 20 = 10, savings = 10
4. Savings 10 parts = Rs. 1200, so the income is Rs. 12000 and personal expenditure = 30% of 12000 = Rs. 3600.

Teacher's Note:
1. Work step by step on the remaining amount each time.
2. Take income as 100 to keep the numbers small.

Question 2: In 2001 the price of article A is 20% more than the price of article B. In 2002 the price of A is 50% more than the price of B. From 2001 to 2002 the price of A has increased by 50%. By what percent has the price of B increased?
(a) 0
(b) 10
(c) 20
(d) 25
Show Answer & Explanation

Answer: (c) 20

Explanation:
1. In 2001 take B = 100, so A = 120
2. In 2002 A = 120 × 1.5 = 180
3. In 2002 A is 1.5 times B, so B = 180/1.5 = 120
4. Increase in B = 20 on 100, that is 20%.

Teacher's Note:
1. Fix the 2001 price of B as 100.
2. The 2002 relation between A and B gives the new price of B.

Question 3: The population of a town increases by 25% annually. If the present population is one crore, what is the difference between the population 3 years ago and that 2 years ago?
(a) 2500000
(b) 1280000
(c) 1560000
(d) 2000000
Show Answer & Explanation

Answer: (b) 1280000

Explanation:
1. Population 2 years ago = 10000000/1.5625 = 6400000
2. Population 3 years ago = 10000000/1.953125 = 5120000
3. Difference = 6400000 − 5120000 = 1280000.

Teacher's Note:
1. To go back one year, divide by 1.25.
2. Subtract the two populations.

Question 4: Ravi has some money. He gave 50% of it to Rupa and 30% to Raju, and 60% of the remaining was donated to a charity. If he is still left with Rs. 8040, how much money did he have initially?
(a) Rs. 100000
(b) Rs. 100500
(c) Rs. 101000
(d) Rs. 101500
Show Answer & Explanation

Answer: (b) Rs. 100500

Explanation:
1. After giving 50% and 30%, 20% of the money is left
2. 40% of that remaining is kept after the 60% donation, so he is left with 0.2 × 0.4 = 8% of the money
3. 8% of the money = 8040, so the money = 8040 × 100/8 = Rs. 100500.

Teacher's Note:
1. Take percentages of the remaining amount, not of the original.
2. Convert the final fraction into a percentage of the start.

Question 5: The ratio of boys and girls in a class is 5 : 3. 20% of the boys and 60% of the girls have passed in first class. What percentage of the class has passed in first class?
(a) 35%
(b) 32%
(c) 34%
(d) 33%
Show Answer & Explanation

Answer: (a) 35%

Explanation:
1. Take 5k boys and 3k girls, so the class has 8k students
2. Boys passing = 0.2 × 5k = k and girls passing = 0.6 × 3k = 1.8k
3. Total passing = 2.8k, and 2.8k/8k × 100 = 35%.

Teacher's Note:
1. Write the ratio as 5k and 3k.
2. Add the passing students before taking the percentage.

Question 6: There are three quantities A, B and C. B is 16 2/3% less than A and C is 14 2/7% more than B. By what percent is A more than C?
(a) 5
(b) 6
(c) 7
(d) 8
Show Answer & Explanation

Answer: (a) 5

Explanation:
1. 16 2/3% = 1/6 and 14 2/7% = 1/7
2. B = (5/6)A and C = (8/7)B = (8/7)(5/6)A = (20/21)A
3. A/C = 21/20, so A is 5% more than C.

Teacher's Note:
1. Change the mixed percentages into fractions.
2. Always compare using the smaller quantity as the base.

Question 7: A's savings are 30% less than B's savings and B's savings are 20% less than C's savings. By what percent are C's savings more than A's savings?
(a) 63 2/7%
(b) 52 1/3%
(c) 64 3/5%
(d) 78 4/7%
Show Answer & Explanation

Answer: (d) 78 4/7%

Explanation:
1. A = 0.7B and B = 0.8C, so A = 0.56C
2. C is more than A by (1 − 0.56)/0.56 × 100 = 44/56 × 100 = 78 4/7%.

Teacher's Note:
1. The percentage more is measured on the smaller quantity, here A.
2. Combine the two relations first.

Question 8: If 55% of the teachers in a school are gents and the number of lady teachers is 90, then the total number of teachers in the school is
(a) 100
(b) 150
(c) 200
(d) 250
Show Answer & Explanation

Answer: (c) 200

Explanation:
1. Lady teachers = 100% − 55% = 45% of the total
2. 45% of the total = 90, so the total = 90 × 100/45 = 200.

Teacher's Note:
1. Find the percentage that corresponds to the known number.
2. Divide the number by that percentage.

Question 9: The population of a city increased at the rate of 20% every year for the last three years. If the present population is 203904, what was the population of the city 3 years ago?
(a) 119000
(b) 118000
(c) 117000
(d) 116000
Show Answer & Explanation

Answer: (b) 118000

Explanation:
1. Present = P × 1.2³ = 1.728P
2. P = 203904/1.728 = 118000.

Teacher's Note:
1. Growth over 3 years multiplies by 1.2 three times.
2. Divide the present value by the factor.

Question 10: The total expenditure of a family in 1920 is Rs. 8000. The cost of living index for 1920, taking 1910 as the base year, is 160. Then the expenditure of the family in 1910 was
(a) Rs. 3000
(b) Rs. 4000
(c) Rs. 5000
(d) Rs. 6000
Show Answer & Explanation

Answer: (c) Rs. 5000

Explanation:
1. Index = (cost in 1920/cost in 1910) × 100 = 160
2. Cost in 1910 = 8000 × 100/160 = Rs. 5000.

Teacher's Note:
1. A cost of living index of 160 means the cost is 1.6 times the base year cost.

Question 11: Kiran's salary was first increased by 30% and then decreased by 30%. If the latest salary is Rs. 2275, what was the original salary?
(a) Rs. 2275
(b) Rs. 2425
(c) Rs. 2600
(d) Rs. 2500
Show Answer & Explanation

Answer: (d) Rs. 2500

Explanation:
1. Final factor = 1.3 × 0.7 = 0.91
2. 0.91 × original = 2275, so the original = 2275/0.91 = Rs. 2500.

Teacher's Note:
1. An equal rise and fall in percent does not return to the original value.

Question 12: In 2000 rice formed 20% of the total foodgrain production in a country. In the next year the total production increased by 20% and rice production was 25% of the total foodgrain production. What is the percentage increase in the production of rice?
(a) 25%
(b) 50%
(c) 40%
(d) 30%
Show Answer & Explanation

Answer: (b) 50%

Explanation:
1. Let the total in 2000 be 100, so rice = 20
2. Next year total = 120 and rice = 25% of 120 = 30
3. Increase = 10 on 20, that is 50%.

Teacher's Note:
1. Compute rice production in both years.
2. Use the old value as base.

Question 13: A manufacturer purchases a second-hand machine for Rs. 60000 and spends some amount on repairs, after which its value goes up to Rs. 90000. If depreciation is 10% per annum, what will be the value of the machine after two years?
(a) Rs. 48600
(b) Rs. 81000
(c) Rs. 67200
(d) Rs. 72900
Show Answer & Explanation

Answer: (d) Rs. 72900

Explanation:
1. Value after repairs = Rs. 90000
2. After two years = 90000 × 0.9 × 0.9 = Rs. 72900.

Teacher's Note:
1. Depreciation starts from the value after repairs.

Question 14: A's expenditure is 20% more than B's expenditure. B's expenditure is 30% less than C's expenditure. By what percentage is A's expenditure less than C's expenditure?
(a) 16%
(b) 12%
(c) 14%
(d) 18%
Show Answer & Explanation

Answer: (a) 16%

Explanation:
1. A = 1.2B and B = 0.7C, so A = 0.84C
2. A is less than C by 16%.

Teacher's Note:
1. Multiply the two factors.

Question 15: Two numbers x and y are in the ratio 5/6 : 3/4. By what percent is x more than y?
(a) 10%
(b) 9.09%
(c) 12.5%
(d) 11.11%
Show Answer & Explanation

Answer: (d) 11.11%

Explanation:
1. x : y = 5/6 : 3/4 = 10 : 9
2. x is more than y by (10 − 9)/9 × 100 = 11.11%.

Teacher's Note:
1. Clear the fractions by multiplying both by 12.

Question 16: Ramu saves 14% of his salary while Ramesh saves 24%. If both get equal salaries and Ramesh saves Rs. 1440, then Ramu's expenditure is
(a) Rs. 5000
(b) Rs. 5160
(c) Rs. 6000
(d) Rs. 7440
Show Answer & Explanation

Answer: (b) Rs. 5160

Explanation:
1. 24% of the salary = 1440, so the salary = Rs. 6000
2. Ramu spends 86% of Rs. 6000 = Rs. 5160.

Teacher's Note:
1. Spending = 100% − savings percentage.

Question 17: The side of square ABCD is 20% longer than the side of square PQRS. By what percentage is the area of ABCD more than the area of PQRS?
(a) 20%
(b) 24%
(c) 40%
(d) 44%
Show Answer & Explanation

Answer: (d) 44%

Explanation:
1. Side ratio = 1.2, so area ratio = 1.44
2. The area of ABCD is 44% more.

Teacher's Note:
1. Area changes with the square of the side.

Question 18: Only two candidates, A and B, contested an election. Out of a total of 20000 votes, 10% were invalid. A won by 3600 votes. What percentage of the valid votes did B secure?
(a) 45%
(b) 40%
(c) 30%
(d) 35%
Show Answer & Explanation

Answer: (b) 40%

Explanation:
1. Valid votes = 90% of 20000 = 18000
2. A + B = 18000 and A − B = 3600, so B = 7200
3. B's share = 7200/18000 × 100 = 40%.

Teacher's Note:
1. Invalid votes are not counted for either candidate.

Question 19: Raju's salary was first increased by 10% and then decreased by 20%. If the latest salary is Rs. 17600, find his original salary.
(a) Rs. 15000
(b) Rs. 10000
(c) Rs. 20000
(d) Rs. 18000
Show Answer & Explanation

Answer: (c) Rs. 20000

Explanation:
1. Final factor = 1.1 × 0.8 = 0.88
2. Original = 17600/0.88 = Rs. 20000.

Teacher's Note:
1. Multiply the factors of successive changes.

Question 20: If A is 50% more than B, then B is less than A by
(a) 33 1/3%
(b) 25%
(c) 50%
(d) 66 2/3%
Show Answer & Explanation

Answer: (a) 33 1/3%

Explanation:
1. Take B = 100, then A = 150
2. B is less than A by 50/150 × 100 = 33 1/3%.

Teacher's Note:
1. The base for percentage less is A, the larger value.

Question 21: Jacob and Mohan save 20% and 40% of their respective incomes. If their expenditures are equal, what is the ratio of the incomes of Mohan and Jacob?
(a) 1 : 2
(b) 3 : 4
(c) 2 : 1
(d) 4 : 3
Show Answer & Explanation

Answer: (d) 4 : 3

Explanation:
1. Jacob spends 80% of his income and Mohan 60% of his
2. 0.8J = 0.6M, so M : J = 0.8 : 0.6 = 4 : 3.

Teacher's Note:
1. Expenditure = income − savings.

Question 22: There are 3 numbers. The first and second numbers are 20% and 40% more than the third number. What percentage is the first number of the sum of the second and the third numbers?
(a) 25%
(b) 50%
(c) 30%
(d) 40%
Show Answer & Explanation

Answer: (b) 50%

Explanation:
1. Take the third = 100: first = 120, second = 140
2. First/(second + third) = 120/240 = 50%.

Teacher's Note:
1. Take the third number as 100.

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Multiple Choice Questions (MCQs) for Class 10 Mathematics Percentage

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FAQs

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