Percentage
- If 35% of a number is 147, what is 60% of that number? Answer: D. 252 Answer: (D) 252 Number = 147 × 100/35 = 420 . 60% of 420 = 252 . (Shortcut: 147 × 60/35 = 252 .) 1
- In an election between two candidates, the winner got 58% of the valid votes and won by 1,920 votes. What was the total number of valid votes? Answer: B. 12,000 Answer: (B) 12,000 Loser got 42%. Margin = 58% - 42% = 16% of valid votes = 1920 . Total = 1920/0.16 = 12000 . 1
- A number is first increased by 20% and then the result is decreased by 25%. What is the net percentage change in the number? Answer: C. 10% decrease Answer: (C) 10% decrease Let the number be 100. After +20%: 120. After −25%: 120 × 0.75 = 90 . Net change = 10% decr... 1
- The population of a town increased by 10% in the first year and decreased by 10% in the second year. If the population at the end of the second year is 39,600, what was it at the beginning of the first year? Answer: A. 40,000 Answer: (A) 40,000 P × 1.1 × 0.9 = 0.99P = 39600 , so P = 40000 . (A 10% rise followed by a 10% fall is a net 1% fall.) 1
- Ramesh spends 65% of his salary and saves the rest. His salary increases by 20% and his expenditure increases by 10%. By approximately what percent do his savings increase? Answer: A. 38.57% Answer: (A) 38.57% Take salary 100: expenditure 65, savings 35. New salary 120, new expenditure 71.5, new savings 48.5. In... 1
- The population of a village increases by 10% every year. If its present population is 12,100, what was its population 2 years ago? Answer: A. 10000 Answer: (A) 10000 Population 2 years ago = 12100/(1.1)² = 12100/1.21 = 10000 . 1
- In an election between two candidates, the winner got 58% of the valid votes and won by 2,400 votes. What was the total number of valid votes? Answer: A. 15000 Answer: (A) 15000 Margin = 58% − 42% = 16% of valid votes = 2400. Valid votes = 2400 ÷ 0.16 = 15,000. 1
- A number is first increased by 20% and the result is then decreased by 15%. If the final value is 8,160, what was the original number? Answer: A. 8000 Answer: (A) 8000 Net factor = 1.20 × 0.85 = 1.02. Original = 8160 ÷ 1.02 = 8000. 1
- In an exam, 65% of the students passed in English, 55% passed in Maths and 15% failed in both. If 245 students passed in both subjects, how many students took the exam? Answer: D. 700 Answer: (D) 700 Passed in at least one = 100 − 15 = 85%. Passed in both = 65 + 55 − 85 = 35%. 35% = 245, so total = 245 × 100... 1
- In an election between two candidates, 20% of the voters on the list did not vote and 500 votes were invalid. The winner got 55% of the valid votes and won by 1,200 votes. How many voters were on the list? Answer: B. 15,625 Answer: (B) 15,625 Margin = 55% − 45% = 10% of valid votes = 1,200, so valid votes = 12,000. Votes cast = 12,000 + 500 inv... 1
- If the numerator of a fraction is increased by 20% and its denominator is decreased by 10%, the fraction becomes \(\frac{16}{21}\). What is the original fraction? Answer: C. 4/7 Answer: (C) 4/7 Shortcut: new fraction = original × 1.2/0.9 = original × 4/3 . Original = 16/21 × 3/4 = 4/7 . Check: 4 × 1.2/... 1
- An ore contains 25% of an alloy, and the alloy contains 90% iron. The rest of the ore has no iron. How many kg of ore are needed to get 45 kg of pure iron? Answer: C. 200 kg Answer: (C) 200 kg Iron in the ore = 90% of 25% = 22.5%. Ore needed = 45 ÷ 0.225 = 200 kg. 1
- What is 35% of 480? Answer: D. 168 Answer: (D) 168 Shortcut: 35% = 10% × 3.5. 10% of 480 = 48, so 35% = 48 × 3.5 = 168. Plain: 35/100 × 480 = 168 . 1
- 45 is what percent of 250? Answer: C. 18% Answer: (C) 18% Shortcut: 250 × 4 = 1000, so 45 × 4 = 180 out of 1000 = 18%. Plain: 45/250 × 100 = 18% . 1
- 12.5% of a number is 75. What is the number? Answer: C. 600 Answer: (C) 600 Shortcut: 12.5% = 1/8 . So the number = 75 × 8 = 600. Plain: number × 0.125 = 75, so number = 75 ÷ 0.125 = 60... 1
- If 1250 is increased by 24%, what is the new value? Answer: B. 1550 Answer: (B) 1550 Shortcut: multiply by 1.24 directly: 1250 × 1.24 = 1550. Plain: 24% of 1250 = 300; 1250 + 300 = 1550. 1
- A's salary is 25% more than B's salary. By what percent is B's salary less than A's? Answer: A. 20% Answer: (A) 20% Shortcut: r/100+r × 100 = 25/125 × 100 = 20% . Plain: let B = 100, then A = 125. B is less by 25 on a base of... 1
- The price of sugar rises by 20%. By what percent must a family reduce its consumption so that its expenditure on sugar stays the same? Answer: C. 162/3 % Answer: (C) 162/3 % Shortcut: reduction = r/100+r × 100 = 20/120 × 100 = 162/3% . Plain: price 100 → 120. To keep spendin... 1
- A number is increased by 10% and the result is then increased by 20%. What is the net percentage increase? Answer: A. 32% Answer: (A) 32% Shortcut (successive change): a + b + ab/100 = 10 + 20 + 200/100 = 32% . Plain: 100 → 110 → 132, a net rise o... 1
- The population of a town is 50,000. It grows by 10% every year. What will it be after 2 years? Answer: A. 60,500 Answer: (A) 60,500 Shortcut: 10% twice = 21% net (10 + 10 + 1). 21% of 50,000 = 10,500, so population = 60,500. Plain: 50,... 1
- In an election between two candidates, the winner got 58% of the valid votes and won by 4,800 votes. How many valid votes were cast? Answer: D. 30,000 Answer: (D) 30,000 Shortcut: winning margin = 58% − 42% = 16% of valid votes. 16% = 4,800, so 100% = 4,800 × 100 ÷ 16 = 30... 1
- In an election, 50,000 votes were cast and 10% of them were invalid. The winning candidate got 60% of the valid votes. How many votes did the losing candidate (the only other candidate) get? Answer: A. 18,000 Answer: (A) 18,000 Valid votes = 90% of 50,000 = 45,000. Loser's share = 100% − 60% = 40% of valid votes = 0.4 × 45,000 =... 1
- A student needs 40% marks to pass. He gets 178 marks and fails by 22 marks. What are the maximum marks? Answer: B. 500 Answer: (B) 500 Shortcut: pass mark = 178 + 22 = 200 = 40% of maximum. Maximum = 200 × 100/40 = 500. Trap: 178/0.4 = 445 igno... 1
- A is 20% less than B and C is 25% more than B. A is what percent of C? Answer: D. 64% Answer: (D) 64% Shortcut: take B = 100. Then A = 80 and C = 125. 80/125 × 100 = 64% . 1