Percentage — Practice

Question 1

What is 62.5% of 480?
(a) 280  (b) 300  (c) 320  (d) 360

Accepted Answer

62.5% = 5/8 (from 12.5% = 1/8).

5/8 × 480 = 5 × 60 = 300.

Answer: (b) 300 — zero long multiplication needed.

Question 2

If 35% of a number exceeds 20% of the same number by 63, the number is:
(a) 400  (b) 420  (c) 450  (d) 480

Accepted Answer

The gap 35% − 20% = 15% of the number = 63.

Number = 63 × 100/15 = 420.

Answer: (b) 420.

Question 3

A's income is 60% more than B's. B's income is what per cent less than A's?
(a) 37.5%  (b) 40%  (c) 60%  (d) 62.5%

Accepted Answer

A = 8/5 B (since 60% = 3/5 more).

So B = 5/8 A → B is 3/8 less = 37.5%.

Answer: (a) 37.5%. The trap option is (c) 60% — % more never equals % less.

Question 4

The price of an article is increased by 25% and then decreased by 12%. The net percentage change is:
(a) +10%  (b) +13%  (c) +11.5%  (d) +12.5%

Accepted Answer

Net = 25 − 12 + (25 × −12)/100 = 13 − 3 = +10%.

Or factors: 5/4 × 22/25 = 110/100 = 1.10.

Answer: (a) +10%.

Question 5

The price of rice rises by 25%. By what per cent should a household cut its consumption so that expenditure rises by only 10%?
(a) 8%  (b) 10%  (c) 12%  (d) 15%

Accepted Answer

Let price factor = 5/4 and target expenditure factor = 11/10.

Consumption factor = (11/10) ÷ (5/4) = 44/50 = 0.88 → a 12% cut.

Answer: (c) 12%. Template: consumption factor = expenditure factor ÷ price factor.

Question 6

The population of a town increases 10% in the first year and 20% in the second year. If the present population (after both increases) is 33,000, what was it two years ago?
(a) 24,000  (b) 25,000  (c) 26,000  (d) 27,500

Accepted Answer

Two years ago × (11/10) × (6/5) = 33,000.

P × 66/50 = 33,000 → P = 33,000 × 50/66 = 25,000.

Answer: (b) 25,000. Work backwards by DIVIDING by the factors — never subtract percentages.

Question 7

In an examination a student who scores 30% fails by 50 marks, while a student who scores 45% gets 25 marks more than the pass mark. The pass mark is:
(a) 150  (b) 200  (c) 175  (d) 190

Accepted Answer

Gap between the two scores = 45% − 30% = 15% of total = 50 + 25 = 75 marks.

Total = 75 ÷ 0.15 = 500.

Pass mark = 30% of 500 + 50 = 150 + 50 = 200.

Answer: (b) 200.

Question 8

In an election between two candidates, 10% of votes cast were invalid. The winner got 60% of the valid votes and won by 3,600 votes. The total votes cast were:
(a) 18,000  (b) 20,000  (c) 22,000  (d) 24,000

Accepted Answer

Margin = 60% − 40% = 20% of valid votes = 3,600 → valid = 18,000.

Valid = 90% of total → total = 18,000 ÷ 0.9 = 20,000.

Answer: (b) 20,000. Two layers: margin on VALID votes, invalid % on TOTAL.

Question 9

A 20% fall in the price of onions lets a buyer purchase 4 kg more for ₹80. The reduced price per kg is:
(a) ₹3.20  (b) ₹4.00  (c) ₹4.80  (d) ₹5.00

Accepted Answer

Money 'freed' on the original quantity = 20% of 80 = ₹16.

This ₹16 buys the extra 4 kg at the NEW price → new price = 16/4 = ₹4.

Answer: (b) ₹4.00. (Original price = 4 ÷ 0.8 = ₹5 — that's option (d), the classic trap.)

Question 10

The length of a rectangle is increased by 30% and its breadth decreased by 20%. The area changes by:
(a) +4%  (b) +6%  (c) −4%  (d) +10%

Accepted Answer

Net = 30 − 20 + (30 × −20)/100 = 10 − 6 = +4%.

Answer: (a) +4%. Area is a product, so the successive-change formula applies directly.

Question 11

In an exam, 42% of candidates failed in English and 52% failed in Science; 17% failed in both. The percentage who passed in both subjects is:
(a) 23%  (b) 25%  (c) 27%  (d) 33%

Accepted Answer

Failed at least one = 42 + 52 − 17 = 77%.

Passed both = 100 − 77 = 23%.

Answer: (a) 23%.

Question 12

16% of 250 + 250% of 16 equals:
(a) 60  (b) 80  (c) 90  (d) 100

Accepted Answer

16% of 250 = 250% of 16 = 40 each (the commutative identity).

40 + 40 = 80.

Answer: (b) 80.

Practice — Percentage

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