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Percentages

Percentage change, successive changes and comparisons.

49 solved questions · 15 easy · 23 medium · 11 hard

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Shortcuts & formulas

  • x% of y = (x/100) x y, and x% of y = y% of x.
  • Successive changes of a% and b%: net change = a + b + ab/100 (use a minus sign for decreases).
  • Increase of p% then decrease of p% gives a net decrease of p^2/100 %.
  • If A is x% more than B, then B is 100x/(100+x) % less than A; if A is x% less than B, then B is 100x/(100-x) % more than A.
  • Price rises by p%: to keep expenditure the same, cut consumption by 100p/(100+p) %.
  • Side of a square up by p%: area rises by 2p + p^2/100 %. Rectangle area change uses the same successive-change formula.
  • Common fractions: 1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%, 3/8 = 37.5%, 5/8 = 62.5%.

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

What is 15% of 360?

  1. A54
  2. B540
  3. C69
  4. D306
Show answer & solution

Answer: A. 54

Solution

15% of 360 = 15/100 x 360 = 54 Answer: 54

Q2.

What is 35% of 840?

  1. A2940
  2. B329
  3. C546
  4. D294
Show answer & solution

Answer: D. 294

Solution

35% of 840 = 35/100 x 840 = 294 Answer: 294

Q3.

What is 8% of 2500?

  1. A2000
  2. B208
  3. C200
  4. D2300
Show answer & solution

Answer: C. 200

Solution

8% of 2500 = 8/100 x 2500 = 200 Answer: 200

Q4.

What percentage of 180 is 45?

  1. A400%
  2. B25%
  3. C35%
  4. D15%
Show answer & solution

Answer: B. 25%

Solution

Percentage = (45/180) x 100 = 25% Answer: 25%

Q5.

What percentage of 120 is 72?

  1. A60%
  2. B166.67%
  3. C70%
  4. D50%
Show answer & solution

Answer: A. 60%

Solution

Percentage = (72/120) x 100 = 60% Answer: 60%

Q6.

Increase 480 by 12.5%. What is the new value?

  1. A492
  2. B600
  3. C552
  4. D540
Show answer & solution

Answer: D. 540

Solution

Increase = 12.5% of 480 = 60 New value = 480 + 60 = 540 Answer: 540

Q7.

Express 7/20 as a percentage.

  1. A285.71%
  2. B40%
  3. C35%
  4. D30%
Show answer & solution

Answer: C. 35%

Solution

7/20 x 100 = 35% Answer: 35%

Q8.

Express 3/8 as a percentage.

  1. A266.67%
  2. B37.5%
  3. C42.5%
  4. D32.5%
Show answer & solution

Answer: B. 37.5%

Solution

3/8 x 100 = 37.5% Answer: 37.5%

Q9.

A shirt priced at ₹650 is sold after an 18% discount. What is the selling price?

  1. A₹533
  2. B₹117
  3. C₹767
  4. D₹632
Show answer & solution

Answer: A. ₹533

Solution

Discount = 18% of 650 = ₹117 Price = 650 - 117 = ₹533 Answer: ₹533

Q10.

If 20% of a number is 84, what is the number?

  1. A168
  2. B104
  3. C840
  4. D420
Show answer & solution

Answer: D. 420

Solution

20% of x = 84 x = 84 x 100/20 = 420 Answer: 420

Shortcut: 20% = 1/5, so the number is 84 x 5 = 420.

Q11.

What is 40% of 25% of 800?

  1. A520
  2. B200
  3. C80
  4. D320
Show answer & solution

Answer: C. 80

Solution

25% of 800 = 200 40% of 200 = 80 Answer: 80

Q12.

Ravi scored 396 marks out of 450. What is his percentage?

  1. A86%
  2. B88%
  3. C90%
  4. D92%
Show answer & solution

Answer: B. 88%

Solution

Percentage = 396/450 x 100 = 88% Answer: 88%

Q13.

The population of a town is 50,000. It rises by 8% in a year. What is the new population?

  1. A54,000
  2. B50,008
  3. C46,000
  4. D54,800
Show answer & solution

Answer: A. 54,000

Solution

Increase = 8% of 50,000 = 4,000 New population = 50,000 + 4,000 = 54,000 Answer: 54,000

Q14.

Meena's earning is 20% more than Asha's. If Asha earns ₹150 per day, how much does Meena earn per day?

  1. A₹120
  2. B₹170
  3. C₹200
  4. D₹180
Show answer & solution

Answer: D. ₹180

Solution

20% of 150 = 30 Meena = 150 + 30 = ₹180 Answer: ₹180

Q15.

What is 12% of 2.5 km, in metres?

  1. A30
  2. B3000
  3. C300
  4. D120
Show answer & solution

Answer: C. 300

Solution

2.5 km = 2,500 m 12% of 2,500 = 300 m Answer: 300 m

Medium questions

Q16.

A price is increased by 20% and then by 10%. What is the net percentage change in the original price?

  1. A30% increase
  2. B32% increase
  3. C34% increase
  4. D32% decrease
Show answer & solution

Answer: B. 32% increase

Solution

Net change = a + b + ab/100 = (20) + (10) + (20)(10)/100 = 30 + (2) = 32% Answer: 32% increase

Shortcut: Take the price as 100 and apply each change in turn.

Q17.

A shop raises a price by 25% and later cuts the new price by 20%. What is the net percentage change in the original price?

  1. ANo change
  2. B5% increase
  3. C45% increase
  4. D2% increase
Show answer & solution

Answer: A. No change

Solution

Net change = a + b + ab/100 = (25) + (-20) + (25)(-20)/100 = 5 + (-5) = 0% Answer: No change

Shortcut: Take the price as 100 and apply each change in turn.

Q18.

The price of a phone falls by 10% in January and by another 10% in February. What is the net percentage change in the original price?

  1. A20% decrease
  2. B20% increase
  3. C17% decrease
  4. D19% decrease
Show answer & solution

Answer: D. 19% decrease

Solution

Net change = a + b + ab/100 = (-10) + (-10) + (-10)(-10)/100 = -20 + (1) = -19% Answer: 19% decrease

Shortcut: Take the price as 100 and apply each change in turn.

Q19.

A bike's price is hiked by 30% and then reduced by 15%. What is the net percentage change in the original price?

  1. A15% increase
  2. B45% increase
  3. C10.5% increase
  4. D12.5% increase
Show answer & solution

Answer: C. 10.5% increase

Solution

Net change = a + b + ab/100 = (30) + (-15) + (30)(-15)/100 = 15 + (-9/2) = 10.5% Answer: 10.5% increase

Shortcut: Take the price as 100 and apply each change in turn.

Q20.

The price of rice rises by 25%. By what percentage must a family cut its consumption to keep its spending unchanged?

  1. A25%
  2. B20%
  3. C12.5%
  4. D80%
Show answer & solution

Answer: B. 20%

Solution

Reduction = 100p/(100+p) % with p = 25 = 2500/125 = 20% Answer: 20%

Q21.

The price of rice rises by 150%. By what percentage must a family cut its consumption to keep its spending unchanged?

  1. A60%
  2. B150%
  3. C75%
  4. D40%
Show answer & solution

Answer: A. 60%

Solution

Reduction = 100p/(100+p) % with p = 150 = 15000/250 = 60% Answer: 60%

Q22.

A is 25% more than B. By what percentage is B less than A?

  1. A25%
  2. B12.5%
  3. C30%
  4. D20%
Show answer & solution

Answer: D. 20%

Solution

Let B = 100, then A = 125 Difference = 25, as a share of A = 25/125 = 20% Answer: 20%

Shortcut: Use 100x/(100+x) = 2500/125 = 20.

Q23.

A's income is 20% less than B's income. By what percentage is B's income more than A's?

  1. A20%
  2. B30%
  3. C25%
  4. D24%
Show answer & solution

Answer: C. 25%

Solution

Let B = 100, then A = 80 B exceeds A by 20, as a share of A = 20/80 = 25% Answer: 25%

Shortcut: Use 100x/(100-x) = 2000/80 = 25.

Q24.

In an election between two candidates, the winner got 55% of the total votes and won by 2,400 votes. Find the total number of votes polled.

  1. A12,000
  2. B24,000
  3. C26,400
  4. D21,600
Show answer & solution

Answer: B. 24,000

Solution

Winner 55%, loser 45% Margin = 10% of total = 2,400 Total = 24,000 Answer: 24,000

Q25.

A student who scores 210 marks fails by 30 marks. The pass mark is 40% of the total. What is the maximum mark?

  1. A600
  2. B525
  3. C450
  4. D750
Show answer & solution

Answer: A. 600

Solution

Pass mark = 210 + 30 = 240 40% of total = 240 Total = 240 x 100/40 = 600 Answer: 600

Q26.

Anil's salary of ₹40,000 is raised by 15% and then by 10%. What is his salary now?

  1. A₹50,000
  2. B₹51,000
  3. C₹46,000
  4. D₹50,600
Show answer & solution

Answer: D. ₹50,600

Solution

After 15% rise: 40,000 x 1.15 = 46,000 After 10% rise: 46,000 x 1.10 = 50,600 Answer: ₹50,600

Q27.

The population of a village, now 80,000, decreases by 5% every year. What will it be after 2 years?

  1. A72,000
  2. B72,800
  3. C72,200
  4. D76,000
Show answer & solution

Answer: C. 72,200

Solution

After year 1: 80,000 x 0.95 = 76,000 After year 2: 76,000 x 0.95 = 72,200 Answer: 72,200

Q28.

A town of 1,20,000 people grows by 10% in the first year and 20% in the second year. What is the population after 2 years?

  1. A1,56,000
  2. B1,58,400
  3. C1,60,000
  4. D1,60,800
Show answer & solution

Answer: B. 1,58,400

Solution

Year 1: 1,20,000 x 1.10 = 1,32,000 Year 2: 1,32,000 x 1.20 = 1,58,400 Answer: 1,58,400

Q29.

A fruit seller sells 40% of his apples in the morning and 25% of the remaining in the afternoon. If 270 apples are left, how many did he have at first?

  1. A600
  2. B450
  3. C675
  4. D540
Show answer & solution

Answer: A. 600

Solution

Let the total be x After morning: 0.60x After afternoon: 0.75 x 0.60x = 0.45x 0.45x = 270, so x = 600 Answer: 600

Q30.

A number 250 is first increased by 20% and then the result is decreased by 20%. What is the final value?

  1. A250
  2. B260
  3. C245
  4. D240
Show answer & solution

Answer: D. 240

Solution

250 x 1.20 = 300 300 x 0.80 = 240 Answer: 240

Shortcut: Net change = -(20^2)/100 = -4%, so 250 x 0.96 = 240.

Q31.

The side of a square is increased by 10%. By what percentage does its area increase?

  1. A10%
  2. B20%
  3. C21%
  4. D11%
Show answer & solution

Answer: C. 21%

Solution

Area is proportional to side^2 New area = 1.1 x 1.1 = 1.21 times the old Increase = 21% Answer: 21%

Q32.

The length of a rectangle is increased by 20% and its breadth is decreased by 10%. What is the percentage change in its area?

  1. A10% increase
  2. B8% increase
  3. C4% increase
  4. D12% increase
Show answer & solution

Answer: B. 8% increase

Solution

New area = 1.2 x 0.9 = 1.08 times the old Change = +8% Answer: 8% increase

Q33.

In an exam Kiran scored 80% in Maths (maximum 200), 70% in Science (maximum 100) and 70% in English (maximum 100). What is his overall percentage?

  1. A75%
  2. B73.33%
  3. C70%
  4. D73%
Show answer & solution

Answer: A. 75%

Solution

Marks: 160 + 70 + 70 = 300 Total maximum = 400 Percentage = 300/400 x 100 = 75% Answer: 75%

Shortcut: Do not average 80, 70 and 70: the papers carry different weights.

Q34.

If 30% of a number is 45 more than 15% of the same number, what is the number?

  1. A150
  2. B200
  3. C450
  4. D300
Show answer & solution

Answer: D. 300

Solution

30% - 15% = 15% of the number = 45 Number = 45 x 100/15 = 300 Answer: 300

Q35.

In a class, 60% of the students are boys. If there are 24 girls, how many boys are in the class?

  1. A24
  2. B40
  3. C36
  4. D48
Show answer & solution

Answer: C. 36

Solution

Girls = 40% of the class = 24 Class = 60 students Boys = 60 - 24 = 36 Answer: 36

Q36.

A is 20% of B and B is 25% of C. A is what percentage of C?

  1. A45%
  2. B5%
  3. C20%
  4. D12.5%
Show answer & solution

Answer: B. 5%

Solution

A = 0.20 B and B = 0.25 C A = 0.20 x 0.25 C = 0.05 C = 5% of C Answer: 5%

Q37.

The price of sugar increases by 20% and a family reduces its consumption by 10%. By what percentage does its spending on sugar change?

  1. A8% increase
  2. B10% increase
  3. C8% decrease
  4. D12% increase
Show answer & solution

Answer: A. 8% increase

Solution

Spend ratio = 1.20 x 0.90 = 1.08 Spending rises by 8% Answer: 8% increase

Q38.

A's marks are 20% more than B's, and B's marks are 25% more than C's. If C scored 160, what did A score?

  1. A232
  2. B200
  3. C224
  4. D240
Show answer & solution

Answer: D. 240

Solution

B = 160 x 1.25 = 200 A = 200 x 1.20 = 240 Answer: 240

Hard questions

Q39.

A price is increased by 20%, then reduced by 25% and then increased by 10%. What is the net percentage change?

  1. A5% increase
  2. B2.5% decrease
  3. C1% decrease
  4. D1% increase
Show answer & solution

Answer: C. 1% decrease

Solution

Take the price as 100 After +20%: 120 After -25%: 90 After +10%: 99 Net change = 99 - 100 = -1% Answer: 1% decrease

Q40.

In an election, 20,000 people are on the voter list. 10% did not vote and 5% of the votes cast were invalid. The winner got 60% of the valid votes. By how many votes did he win?

  1. A3,600
  2. B3,420
  3. C3,000
  4. D3,780
Show answer & solution

Answer: B. 3,420

Solution

Votes cast = 90% of 20,000 = 18,000 Valid = 95% of 18,000 = 17,100 Winner = 60% of 17,100 = 10,260; loser = 6,840 Margin = 3,420 Answer: 3,420

Q41.

A town has 50,000 people. After a year the male population rose by 5% and the female population by 10%, and the town now has 54,000 people. How many females were there originally?

  1. A30,000
  2. B20,000
  3. C25,000
  4. D33,000
Show answer & solution

Answer: A. 30,000

Solution

Let females = f, males = 50,000 - f 1.05(50,000 - f) + 1.10 f = 54,000 52,500 + 0.05 f = 54,000 f = 1,500/0.05 = 30,000 Answer: 30,000

Q42.

A price rises by x% and then falls by x%, and ends 4% below the original price. Find x.

  1. A10%
  2. B2%
  3. C4%
  4. D20%
Show answer & solution

Answer: D. 20%

Solution

Net change = -x^2/100 = -4 x^2 = 400 x = 20 Answer: 20%

Q43.

Fresh fruit contains 80% water and dry fruit contains 20% water. How many kg of dry fruit can be obtained from 100 kg of fresh fruit?

  1. A20 kg
  2. B26.6667 kg
  3. C25 kg
  4. D40 kg
Show answer & solution

Answer: C. 25 kg

Solution

Solid in fresh fruit = 20% of 100 = 20 kg In dry fruit the solid is 80% Dry fruit = 20/0.80 = 25 kg Answer: 25 kg

Q44.

A man spends 80% of his income. His income rises by 20% and his expenditure rises by 10%. By what percentage do his savings increase?

  1. A30%
  2. B60%
  3. C10%
  4. D40%
Show answer & solution

Answer: B. 60%

Solution

Income 100, expenditure 80, savings 20 New income 120, new expenditure 88, savings 32 Increase = 12/20 = 60% Answer: 60%

Q45.

In a class, 70% passed Maths, 80% passed English and 10% failed in both. What percentage passed both subjects?

  1. A60%
  2. B50%
  3. C70%
  4. D56%
Show answer & solution

Answer: A. 60%

Solution

Failed Maths 30%, failed English 20%, failed both 10% Failed at least one = 30 + 20 - 10 = 40% Passed both = 100 - 40 = 60% Answer: 60%

Q46.

x is 20% of y, and y is 50% more than z. x is what percentage of z?

  1. A25%
  2. B10%
  3. C70%
  4. D30%
Show answer & solution

Answer: D. 30%

Solution

y = 1.5 z x = 0.2 y = 0.2 x 1.5 z = 0.3 z Answer: 30%

Q47.

A's salary is 20% less than B's, and B's salary is 25% less than C's. If C earns ₹80,000, how much does A earn?

  1. A₹44,000
  2. B₹64,000
  3. C₹48,000
  4. D₹52,000
Show answer & solution

Answer: C. ₹48,000

Solution

B = 0.75 x 80,000 = 60,000 A = 0.80 x 60,000 = 48,000 Answer: ₹48,000

Q48.

The length of a rectangle is increased by 25%. By what percentage must its breadth be decreased so that its area increases by only 20%?

  1. A5%
  2. B4%
  3. C20%
  4. D12.5%
Show answer & solution

Answer: B. 4%

Solution

Required factor for breadth = 1.20/1.25 = 0.96 Breadth must decrease by 4% Answer: 4%

Q49.

The radius of a circle is increased by 20%. By what percentage does its area increase?

  1. A44%
  2. B20%
  3. C40%
  4. D22%
Show answer & solution

Answer: A. 44%

Solution

Area is proportional to radius^2 New area = 1.2 x 1.2 = 1.44 times Increase = 44% Answer: 44%

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