Practice Questions
Concept Explanation
When principal, simple interest, and time are known, find the rate using the rearranged SI formula.
Key Formula
R = (100 × SI) / (P × T)
Example
P = Rs. 5,000, SI = Rs. 1,000, T = 2 years. R = (100 × 1000)/(5000 × 2) = 10%.
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Q1 EasyA sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?ExplanationSI = Amount − Principal = 15500 − 12500 = Rs. 3,000. Formula: R = (100 × SI) / (P × T) = (100 × 3000) / (12500 × 4) = 300000 / 50000 = 6%. Hence the rate is 6%.
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Q2 EasyAt what rate percent per annum will a sum of money double itself in 12 years at SI?ExplanationWhen a sum doubles at SI, SI = P. Formula: P = (P × R × 12) / 100 ⇒ 100 = 12R ⇒ R = 100/12 = 25/3 = 8⅓%. Hence the rate is 8⅓%.
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Q3 EasyP = Rs. 5,000, SI = Rs. 1,000, T = 2 years. The rate is:ExplanationFormula: R = (100 × SI) / (P × T) = (100 × 1000) / (5000 × 2) = 100000 / 10000 = 10%. Hence the rate is 10%.
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Q4 EasyP = Rs. 8,000, SI = Rs. 960, T = 3 years. Rate is:ExplanationFormula: R = (100 × SI) / (P × T) = (100 × 960) / (8000 × 3) = 96000 / 24000 = 4%. Hence the rate is 4%.
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Q5 EasyP = Rs. 10,000, SI = Rs. 1,500, T = 3 years. Rate is:ExplanationFormula: R = (100 × SI) / (P × T) = (100 × 1500) / (10000 × 3) = 150000 / 30000 = 5%. Hence the rate is 5%.
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Q6 MediumReena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?ExplanationLet rate = R% and time = R years. Formula: SI = (P × R × T) / 100 ⇒ 432 = (1200 × R × R) / 100 ⇒ 12R² = 432 ⇒ R² = 36 ⇒ R = 6 (taking the positive root). Hence the rate of interest is 6%.
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Q7 MediumA lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:ExplanationFormula: SI = (P × R × T) / 100. (5000 × R × 2)/100 + (3000 × R × 4)/100 = 2200 ⇒ 100R + 120R = 2200 ⇒ 220R = 2200 ⇒ R = 10. Hence the rate is 10%.
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Q8 MediumA sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:ExplanationSI for 3 years = 12005 − 9800 = Rs. 2,205. SI for 1 year = 2205 / 3 = Rs. 735. SI for 5 years = 735 × 5 = Rs. 3,675. Principal = 9800 − 3675 = Rs. 6,125. Rate R = (100 × 735) / (6125 × 1) = 73500 / 6125 = 12%. Hence the rate is 12%.
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Q9 MediumIn a campus drill, P = Rs. 12,000, SI = Rs. 3,600, T = 3 years. Rate is:ExplanationFormula: R = (100 × SI) / (P × T) = (100 × 3600) / (12000 × 3) = 360000 / 36000 = 10%. Hence the rate is 10%.
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Q10 MediumP = Rs. 15,000, SI = Rs. 4,500, T = 2 years. Rate is:ExplanationFormula: R = (100 × SI) / (P × T) = (100 × 4500) / (15000 × 2) = 450000 / 30000 = 15%. Hence the rate is 15%.
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Q11 HardThe simple interest on a sum of money is 4/9 of the principal. Find the rate percent and time if both are equal.ExplanationLet rate = time = R. Formula: SI = (P × R × T) / 100 ⇒ (4/9)P = (P × R × R) / 100 ⇒ 4/9 = R²/100 ⇒ R² = 400/9 ⇒ R = 20/3 = 6⅔. So rate = 6⅔% and time = 6⅔ years (i.e., 6 years 8 months). Hence the answer is 6⅔% and 6⅔ years.
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Q12 HardAn automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:ExplanationLet principal = Rs. 100. SI for first 6 months = (100 × 10 × 1/2) / 100 = Rs. 5. New principal for next 6 months = 105. SI for next 6 months = (105 × 10 × 1/2) / 100 = Rs. 5.25. Amount after 1 year = 100 + 5 + 5.25 = Rs. 110.25. Effective rate = 10.25%. Hence the answer is 10.25%.
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Q13 HardP = Rs. 9,000, SI = Rs. 1,350, T = 2.5 years. Rate is:ExplanationFormula: R = (100 × SI) / (P × T) = (100 × 1350) / (9000 × 2.5) = 135000 / 22500 = 6%. Hence the rate is 6%.
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Q14 HardP = Rs. 20,000, SI = Rs. 5,000, T = 2 years. Rate is:ExplanationFormula: R = (100 × SI) / (P × T) = (100 × 5000) / (20000 × 2) = 500000 / 40000 = 12.5%. Hence the rate is 12.5%.
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DS1 Easy
What is the rate of interest?
Statement IPrincipal is Rs. 5,000 and SI is Rs. 1,000 for 2 years.
Statement IITime is 2 years only (principal and SI not given).
ExplanationFormula: R = (100 × SI) / (P × T). Statement I alone: R = (100 × 1000) / (5000 × 2) = 10%. Statement II alone is insufficient. Answer: A. -
DS2 Easy
What is the rate?
Statement IPrincipal is Rs. 8,000.
Statement IISI is Rs. 960 for 3 years.
ExplanationFormula: R = (100 × SI) / (P × T). Statement I alone lacks SI and T. Statement II alone lacks P. Together: R = (100 × 960) / (8000 × 3) = 4%. Both are needed. Answer: C.
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DS3 Medium
During an online screening, find the rate. What is the rate?
Statement ISI is Rs. 1,500.
Statement IIPrincipal is Rs. 10,000 and time is 3 years.
ExplanationFormula: R = (100 × SI) / (P × T). Statement I alone lacks P and T. Statement II alone lacks SI. Together: R = (100 × 1500) / (10000 × 3) = 5%. Both are needed. Answer: C. -
DS4 Medium
An HR quiz asks a comparison. Is the rate greater than 8%?
Statement IP = Rs. 12,000, SI = Rs. 3,600 and T = 3 years.
Statement IIOnly the time is 3 years.
ExplanationFormula: R = (100 × SI) / (P × T). Statement I: R = (100 × 3600) / (12000 × 3) = 10%, which is greater than 8%. Statement II alone is insufficient. Answer: A.