Practice Questions
Concept Explanation
Placement questions often combine simple interest, compound interest, rate changes, and comparisons in a single problem.
Strategy
- Identify whether the problem uses SI or CI.
- Convert time to years (months ÷ 12, days ÷ 365).
- For comparisons, calculate both amounts separately.
- Use difference formulas when CI − SI is asked for 2 or 3 years.
Example
Rs. 10,000 at 10% SI for 2 years gives amount Rs. 12,000. Same at CI annually gives Rs. 12,100.
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Q1 EasyA sum doubles itself under SI in 8 years. The rate of interest is:ExplanationWhen SI = P, (P × R × T)/100 = P ⇒ RT = 100 ⇒ R = 100/T = 100/8 = 12.5%. Hence the rate is 12.5%.
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Q2 EasyRs. 10,000 is invested at 10% SI for 2 years and the same sum at 10% CI annually for 2 years. CI exceeds SI by:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 10000 × 0.01 = Rs. 100. Check: SI = 2000; CI = 2100. Hence the answer is Rs. 100.
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Q3 EasyThe difference between CI and SI on Rs. 8,000 for 2 years at 5% per annum is:ExplanationFormula for 2 years: CI − SI = P(R/100)^2. Difference = 8000 × (5/100)^2 = 8000 × 0.0025 = Rs. 20. Hence the answer is Rs. 20.
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Q4 EasySI on Rs. 5,000 for 4 years at 10% exceeds SI on the same sum for 4 years at 6% by:ExplanationDifference = [P × (10 − 6) × 4]/100 = (5000 × 4 × 4)/100 = Rs. 800. Hence the answer is Rs. 800.
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Q5 MediumA sum of money placed at CI doubles itself in 5 years. In how many years will it amount to 8 times itself?ExplanationUnder CI, if the sum doubles in 5 years, then in successive 5-year blocks it becomes 2×, 4×, 8×, …. To become 8 times (= 2^3 times), it needs 3 doubling periods = 3 × 5 = 15 years. Hence the answer is 15 years.
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Q6 MediumSimple interest on a sum at 12% for 4 years is Rs. 4800 more than SI at 8% for 4 years. Principal:ExplanationDifference of SI = [P × (12 − 8) × 4]/100 = 4800. So (P × 4 × 4)/100 = 4800 ⇒ 16P = 4,80,000 ⇒ P = Rs. 30,000. Hence the principal is Rs. 30,000.
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Q7 MediumThe present worth of Rs. 169 due in 2 years at 4% per annum compound interest is:ExplanationFormula: Present worth = Amount / (1 + R/100)^T. PW = 169 / (1.04)^2 = 169 / 1.0816 = Rs. 156.25. Check: 156.25 × 1.0816 = 169. Hence the answer is Rs. 156.25.
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Q8 MediumA sum of money becomes 4 times itself in 2 years at CI. In how many years will it become 16 times itself at the same rate?ExplanationIf (1 + R/100)^2 = 4, then (1 + R/100)^4 = 4^2 = 16. Therefore time required = 4 years (two successive 2-year growth periods). Hence the answer is 4 years.
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Q9 HardA sum amounts to Rs. 2916 in 2 years and Rs. 3149.28 in 3 years at CI. Rate:ExplanationInterest in the 3rd year = 3149.28 − 2916 = Rs. 233.28. This interest is earned on the amount after 2 years. Rate R = (233.28 / 2916) × 100 = 8%. Hence the rate is 8%.
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Q10 HardCI for 2 years = Rs. 3150, SI for 2 years = Rs. 3000 on same sum same rate. Find rate and principal.ExplanationCI − SI for 2 years = 3150 − 3000 = Rs. 150 = P(R/100)^2. Also SI = (P × R × 2)/100 = 3000 ⇒ PR/50 = 3000 ⇒ PR = 1,50,000. From P R^2 / 10000 = 150 ⇒ P R^2 = 15,00,000. Divide: R = 15,00,000 / 1,50,000 = 10. Then P = 1,50,000 / 10 = Rs. 15,000. Hence R = 10% and P = Rs. 15,000.
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Q11 HardA sum amounts to Rs. 4,840 in 2 years and to Rs. 5,324 in 3 years at CI annually. The rate is:ExplanationInterest in the 3rd year = 5324 − 4840 = Rs. 484. Rate = (484 / 4840) × 100 = 10%. Hence the rate is 10%.
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Q12 HardAt what rate of CI will a sum become 27 times itself in 3 years?ExplanationA/P = (1 + R/100)^T ⇒ 27 = (1 + R/100)^3 ⇒ 1 + R/100 = 3 ⇒ R/100 = 2 ⇒ R = 200%. Hence the rate is 200%.
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Q13 HardSI on a sum for 3 years at 10% is Rs. 1,550 less than CI on the same sum for 3 years at 10%. The principal is:ExplanationFormula for 3 years: CI − SI = P(R/100)^2 × (3 + R/100). 1550 = P × 0.01 × 3.1 = 0.031 P ⇒ P = 1550 / 0.031 = Rs. 50,000. Check: SI = 15000; CI = 50000 × 1.331 − 50000 = 16550; difference = 1550. Hence the principal is Rs. 50,000.
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Q14 HardA certain sum at CI becomes Rs. 7,290 in 3 years at 20% per annum. The principal is:ExplanationFormula: P = A / (1 + R/100)^T. P = 7290 / (1.2)^3 = 7290 / 1.728 = Rs. 4,218.75. Hence the principal is Rs. 4,218.75.
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DS1 Medium
In how many years will a sum become 8 times itself at CI?
Statement IThe sum doubles itself in 5 years at compound interest.
Statement IIThe interest is compounded annually at a fixed rate.
ExplanationIf money doubles in 5 years at CI, then 8 times (= 2^3) takes 3 × 5 = 15 years. Statement I alone is sufficient. Statement II alone does not give the doubling period. Answer: A. -
DS2 Medium
Find the principal from SI rate comparison. What is the principal?
Statement ISI at 12% for 4 years exceeds SI at 8% for 4 years by Rs. 4,800.
Statement IIThe time period for both rates is 4 years.
ExplanationStatement I alone: [P × 4 × 4]/100 = 4800 ⇒ P = 30,000. Statement II alone does not give the SI difference. Statement I alone is sufficient. Answer: A.
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DS3 Hard
A company screening item asks for the CI rate. What is the rate?
Statement IA sum amounts to Rs. 2,916 in 2 years and Rs. 3,149.28 in 3 years at CI.
Statement IICompounding is annual.
ExplanationStatement I alone: third-year interest = 3149.28 − 2916 = 233.28; R = (233.28/2916) × 100 = 8%. Statement II alone is incomplete. Statement I alone is sufficient. Answer: A. -
DS4 Hard
What are the rate and principal?
Statement ICI for 2 years is Rs. 3,150 and SI for 2 years is Rs. 3,000 on the same sum at the same rate.
Statement IIInterest is compounded annually.
ExplanationStatement I alone: CI − SI = 150 = P(R/100)^2 and SI = 3000 = 2PR/100 ⇒ R = 10%, P = 15,000. Statement II alone is incomplete. Statement I alone is sufficient. Answer: A.