Quantitative aptitude
- What is the effective annual rate of interest for a nominal rate of 10% per annum compounded half-yearly? Answer: B. 10.25% Answer: (B) 10.25% 5% for two half-years: 5 + 5 + 5 × 5/100 = 10.25%. 1
- The difference between compound interest and simple interest on a sum for 2 years at 5% per annum is ₹15. What is the sum? Answer: C. ₹6000 Answer: (C) ₹6000 CI − SI = P(5/100)² = P/400 = 15, so P = ₹6000. 1
- The simple interest on a sum is one-fourth of the sum, and the rate of interest per annum equals the number of years. What is the rate? Answer: D. 5% Answer: (D) 5% SI = P × R × R/100 = P/4 , so R² = 25 and R = 5%. 1
- What equal annual instalment will pay off a debt of ₹3,630 due in 3 years at 10% per annum simple interest? Answer: C. ₹1100 Answer: (C) ₹1100 Instalments paid at the end of years 1, 2 and 3 earn interest for 2, 1 and 0 years until the due date. So... 1
- A loan of ₹2,200 is to be repaid in two equal annual instalments at 20% per annum compound interest. What is each instalment? Answer: D. ₹1440 Answer: (D) ₹1440 The present values of the instalments add up to the loan: x/1.2 + x/1.2² = 2200 . x × 1.2 + 1/1.44 = 2200... 1
- ₹2,210 is divided between A and B so that A's share after 3 years equals B's share after 5 years, both at 10% per annum compound interest. What is A's share? Answer: B. ₹1210 Answer: (B) ₹1210 A(1.1)³ = B(1.1)⁵ , so A/B = (1.1)² = 121/100 . A's share = 121/221 × 2210 = ₹1210 (and B's = ₹1000). 1
- The compound interest on a sum for the 2nd year is ₹1,320 and for the 3rd year is ₹1,452. What is the sum? Answer: A. ₹12,000 Answer: (A) ₹12,000 Rate = 1452 - 1320/1320 × 100 = 10% . 2nd-year interest = P × 1.1 × 0.1 = 0.11P = 1320, so P = ₹12,00... 1
- The simple interest on a sum for 2 years is ₹600 and the compound interest on the same sum at the same rate for 2 years is ₹630. What is the sum? Answer: A. ₹3000 Answer: (A) ₹3000 SI for one year = ₹300. The extra ₹30 in CI is interest on the first year's ₹300, so the rate = 30 ÷ 300... 1
- What is the simple interest on ₹5,000 at 8% per annum for 3 years? Answer: C. ₹1200 Answer: (C) ₹1200 SI = P × R × T/100 = 5000 × 8 × 3/100 = ₹1200. 1
- A sum of money amounts to ₹7,800 in 3 years at 10% per annum simple interest. What is the sum? Answer: A. ₹6000 Answer: (A) ₹6000 In 3 years the sum grows by 30%, so the amount = 1.3 × P. P = 7800 ÷ 1.3 = ₹6000. Trap: taking 30% off ₹7... 1
- At what rate of simple interest will a sum of money double itself in 8 years? Answer: D. 12.5% Answer: (D) 12.5% Doubling means SI = P, i.e. 100% in 8 years. Rate = 100 ÷ 8 = 12.5% per annum. 1
- What is the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually? Answer: A. ₹2100 Answer: (A) ₹2100 Shortcut: 10% for 2 years = 21% effective (10 + 10 + 1). CI = 21% of 10,000 = ₹2100. Plain: 10,000 × 1.1²... 1
- ₹1,800 is divided between two friends in the ratio 4 : 5. What is the larger share? Answer: D. ₹1000 Answer: (D) ₹1000 Shortcut: 4 + 5 = 9 parts, 1 part = 1800 ÷ 9 = 200. Larger share = 5 × 200 = ₹1000. 1
- Find the fourth proportional to 6, 8 and 15. Answer: C. 20 Answer: (C) 20 If 6 : 8 = 15 : x, then x = 8 × 15/6 = 20 . 1
- What is the mean proportional between 9 and 16? Answer: C. 12 Answer: (C) 12 Mean proportional = √(9 × 16) = √(144) = 12 . Trap: 12.5 is the average, not the mean proportional. 1
- If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c. Answer: A. 8 : 12 : 15 Answer: (A) 8 : 12 : 15 Shortcut: make b equal. Multiply the first ratio by 4 and the second by 3: a : b = 8 : 12 and... 1
- What is the third proportional to 4 and 12? Answer: A. 36 Answer: (A) 36 If 4 : 12 = 12 : x, then x = 12²/4 = 36 . 1
- Two numbers are in the ratio 5 : 7 and their sum is 168. What is their difference? Answer: B. 28 Answer: (B) 28 Shortcut: 12 parts = 168, so 1 part = 14. Difference = 7 − 5 = 2 parts = 28. 1
- What is the compounded ratio of 2 : 3, 6 : 11 and 11 : 2? Answer: B. 2 : 1 Answer: (B) 2 : 1 Multiply the antecedents and the consequents: 2 × 6 × 11/3 × 11 × 2 = 132/66 = 2/1 . Compounded ratio = 2... 1
- In a class the ratio of boys to girls is 7 : 5. If there are 84 boys, how many students are there in all? Answer: C. 144 Answer: (C) 144 1 part = 84 ÷ 7 = 12. Total = 12 parts = 12 × 12 = 144. 1
- The incomes of A and B are in the ratio 5 : 4 and their expenditures are in the ratio 3 : 2. If each of them saves ₹1,600, what is A's income? Answer: D. ₹4000 Answer: (D) ₹4000 Let incomes be 5x, 4x and expenditures 3y, 2y. Then 5x − 3y = 1600 and 4x − 2y = 1600. From the second, y... 1
- A bag contains ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8. The total value is ₹210. How many 50-paise coins are there? Answer: B. 126 Answer: (B) 126 Shortcut: convert the number ratio into a value ratio: 5 × 1 : 6 × 0.5 : 8 × 0.25 = 5 : 3 : 2, i.e. 10 value... 1
- What number must be added to each of 6, 10, 14 and 22 so that the resulting numbers are in proportion? Answer: A. 2 Answer: (A) 2 Let x be added. Then (6 + x)(22 + x) = (10 + x)(14 + x). 132 + 28x = 140 + 24x, so 4x = 8 and x = 2. Check: 8 : 1... 1
- Two numbers are in the ratio 3 : 5. If 10 is added to each, the ratio becomes 5 : 7. What is the smaller number? Answer: A. 15 Answer: (A) 15 Let the numbers be 3k and 5k. Then 7(3k + 10) = 5(5k + 10), so 21k + 70 = 25k + 50 and k = 5. Smaller number =... 1