Set A Solutions

A1. Answer: (c) Rs. 2,400 Method: Direct SI formula. SI = PRT/100 = (7500 × 8 × 4)/100 = 240000/100 = Rs. 2,400. Option (b) Rs. 2,200 is what you get if you mistakenly use T = 3 instead of 4 — always re-check the value you copied for time before calculating.

A2. Answer: (d) Rs. 6,720 Method: Compute SI, then add to principal for the amount. SI = (6000 × 6 × 2)/100 = Rs. 720. Amount = 6000 + 720 = Rs. 6,720. A student who forgets to add back the principal and reports only the SI (Rs. 720) would wrongly eliminate every option here, which is itself a useful self-check that the SI step was done correctly.

A3. Answer: (b) 6% Method: Rearranged SI formula for rate. R = (SI × 100)/(P × T) = (960 × 100)/(4000 × 4) = 96000/16000 = 6%.

A4. Answer: (b) Rs. 5,000 Method: Rearranged SI formula for principal. P = (SI × 100)/(R × T) = (1500 × 100)/(5 × 6) = 150000/30 = Rs. 5,000.

A5. Answer: (b) 6% Method: First extract SI from the amount, then apply the rate formula. SI = 6500 − 5000 = Rs. 1,500. R = (1500 × 100)/(5000 × 5) = 150000/25000 = 6%. Never plug the full amount (6500) into the SI formula in place of SI itself — that is the most common slip on this question type.

A6. Answer: (c) Rs. 2,520 Method: Basic annual CI. A = 12000 × (1.1)² = 12000 × 1.21 = Rs. 14,520. CI = 14520 − 12000 = Rs. 2,520. Cross-check using the shortcut: CI for 2 years at 10% on Rs. 100 is Rs. 21 (Trick 2), so on Rs. 12,000 it is 12,000 × 21/100 = Rs. 2,520 — matches instantly.

A7. Answer: (c) Rs. 2,050 Method: Basic annual CI. A = 20000 × (1.05)² = 20000 × 1.1025 = Rs. 22,050. CI = 22050 − 20000 = Rs. 2,050.

A8. Answer: (c) Rs. 2,648 Method: Basic 3-year annual CI. A = 8000 × (1.1)³ = 8000 × 1.331 = Rs. 10,648. CI = 10648 − 8000 = Rs. 2,648. Option (a) Rs. 2,480 would result from mistakenly using simple interest at 10% for 3 years (2400) plus a small miscalculation — a reminder to double-check you are applying compound, not simple, growth.

A9. Answer: (b) Rs. 24 Method: Direct 2-year difference shortcut. Diff = PR²/10000 = (15000 × 16)/10000 = 240000/10000 = Rs. 24.

A10. Answer: (b) Rs. 20 Method: Direct 2-year difference shortcut. Diff = PR²/10000 = (8000 × 25)/10000 = 200000/10000 = Rs. 20.

A11. Answer: (c) Rs. 12,100 Method: Convert to half-yearly terms first. 20% p.a. half-yearly → rate per half-year = 10%, periods = 2. A = 10000 × (1.1)² = 10000 × 1.21 = Rs. 12,100. Option (b) Rs. 12,000 is the trap for students who mistakenly apply the annual rate directly without halving it and doubling the periods.

A12. Answer: (b) Rs. 19,360 Method: Basic annual CI amount formula. A = 16000 × (1.1)² = 16000 × 1.21 = Rs. 19,360.

A13. Answer: (c) Rs. 20 Method: Direct 2-year difference shortcut. Diff = PR²/10000 = (2000 × 100)/10000 = Rs. 20.

A14. Answer: (b) 6% Method: Rearranged SI formula for rate. R = (SI × 100)/(P × T) = (2304 × 100)/(9600 × 4) = 230400/38400 = 6%.

A15. Answer: (c) Rs. 1,040 Method: Basic annual CI. A = 6250 × (1.08)² = 6250 × 1.1664 = Rs. 7,290. CI = 7290 − 6250 = Rs. 1,040.

A16. Answer: (c) Rs. 6,000 Method: Rearranged SI-amount formula. Amount = P(1 + RT/100), so 7440 = P(1 + 24/100) = P × 1.24. P = 7440/1.24 = Rs. 6,000.

A17. Answer: (c) Rs. 3,960 Method: Basic annual CI. A = 9000 × (1.2)² = 9000 × 1.44 = Rs. 12,960. CI = 12960 − 9000 = Rs. 3,960.

A18. Answer: (b) Rs. 2,000 Method: Reverse-apply the 2-year difference shortcut. 45 = P × 15²/10000 = P × 225/10000. P = 45 × 10000/225 = Rs. 2,000.

A19. Answer: (c) Rs. 1,700 Method: Convert to half-yearly terms first. 25% p.a. half-yearly → rate per half-year = 12.5%, periods = 2. A = 6400 × (1.125)² = 6400 × 1.265625 = Rs. 8,100. CI = 8100 − 6400 = Rs. 1,700.

A20. Answer: (b) 6 years Method: Rearranged SI formula for time. T = (SI × 100)/(P × R) = (1080 × 100)/(3000 × 6) = 108000/18000 = 6 years.