Practice Questions
Concept Explanation
When principal, rate, and simple interest are known, find time using the rearranged formula.
Key Formula
T = (100 × SI) / (P × R)
Example
P = Rs. 5,000, SI = Rs. 1,500, R = 10%. T = (100 × 1500)/(5000 × 10) = 3 years.
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Q1 EasyHow much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?ExplanationFormula: T = (100 × SI) / (P × R). T = (100 × 81) / (450 × 4.5) = 8100 / 2025 = 4 years. Hence the time is 4 years.
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Q2 EasyIn how many years will a sum of money become three times itself at 10% per annum simple interest?ExplanationTo become 3 times, Amount = 3P ⇒ SI = 2P. Formula: 2P = (P × 10 × T) / 100 ⇒ 200 = 10T ⇒ T = 20 years. Hence the time is 20 years.
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Q3 EasyP = Rs. 5,000, SI = Rs. 1,500, R = 10%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 1500) / (5000 × 10) = 150000 / 50000 = 3 years. Hence the time is 3 years.
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Q4 EasyP = Rs. 8,000, SI = Rs. 1,600, R = 5%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 1600) / (8000 × 5) = 160000 / 40000 = 4 years. Hence the time is 4 years.
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Q5 EasyIn a screening test, P = Rs. 6,000, SI = Rs. 720, R = 4%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 720) / (6000 × 4) = 72000 / 24000 = 3 years. Hence the time is 3 years.
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Q6 EasyP = Rs. 15,000, SI = Rs. 4,500, R = 10%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 4500) / (15000 × 10) = 450000 / 150000 = 3 years. Hence the time is 3 years.
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Q7 MediumA sum of money doubles itself in 8 years at SI. In how many years will it become 4 times at SI?ExplanationTo double, SI = P in 8 years. To become 4 times, SI must equal 3P. Since SI ∝ T at fixed P and R, time required = 8 × 3 = 24 years. Alternatively, from SI = P in 8 years, RT/100 = 1 ⇒ R = 100/8 = 12.5%; for SI = 3P, T = (100 × 3) / 12.5 = 24 years. Hence the answer is 24 years.
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Q8 MediumA sum of money becomes five times itself in 20 years at simple interest. In how many years will it become three times at the same rate?ExplanationTo become 5 times, SI = 4P in 20 years ⇒ RT/100 = 4 ⇒ R = 400/20 = 20%. To become 3 times, SI = 2P ⇒ 2P = (P × 20 × T) / 100 ⇒ 200 = 20T ⇒ T = 10 years. Hence the time is 10 years.
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Q9 MediumAt what time will the simple interest on Rs. 800 at 5% per annum be equal to the simple interest on Rs. 1,000 at 4% for 4 years?ExplanationSI on Rs. 1000 at 4% for 4 years = (1000 × 4 × 4) / 100 = Rs. 160. For Rs. 800 at 5%: 160 = (800 × 5 × T) / 100 ⇒ 160 = 40T ⇒ T = 4 years. Hence the time is 4 years.
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Q10 MediumP = Rs. 10,000, SI = Rs. 3,000, R = 6%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 3000) / (10000 × 6) = 300000 / 60000 = 5 years. Hence the time is 5 years.
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Q11 MediumP = Rs. 12,000, SI = Rs. 4,800, R = 8%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 4800) / (12000 × 8) = 480000 / 96000 = 5 years. Hence the time is 5 years.
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Q12 HardThe simple interest on a sum of money will be Rs. 600 after 5 years. If the principal is trebled after 2 years, what will be the total interest at the end of the 5th year?ExplanationOriginal SI for 5 years = Rs. 600 ⇒ SI per year on original P = 600/5 = Rs. 120. For first 2 years, SI = 120 × 2 = Rs. 240. After 2 years principal becomes 3P, so annual SI becomes 3 × 120 = Rs. 360. For next 3 years, SI = 360 × 3 = Rs. 1,080. Total interest = 240 + 1080 = Rs. 1,320. Hence the answer is Rs. 1,320.
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Q13 HardP = Rs. 20,000, SI = Rs. 8,000, R = 10%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 8000) / (20000 × 10) = 800000 / 200000 = 4 years. Hence the time is 4 years.
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Q14 HardP = Rs. 25,000, SI = Rs. 7,500, R = 12%. Time is:ExplanationFormula: T = (100 × SI) / (P × R) = (100 × 7500) / (25000 × 12) = 750000 / 300000 = 2.5 years. Hence the time is 2.5 years.
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DS1 Easy
What is the time period?
Statement IP = Rs. 5,000, SI = Rs. 1,500 and R = 10%.
Statement IIOnly the rate is 10% per annum.
ExplanationFormula: T = (100 × SI) / (P × R). Statement I alone: T = (100 × 1500) / (5000 × 10) = 3 years. Statement II alone is insufficient. Answer: A. -
DS2 Easy
For the loan tenure. What is the time?
Statement IPrincipal is Rs. 8,000.
Statement IISI is Rs. 1,600 at 5% per annum.
ExplanationFormula: T = (100 × SI) / (P × R). Statement I alone lacks SI and R. Statement II alone lacks P. Together: T = (100 × 1600) / (8000 × 5) = 4 years. Both are needed. Answer: C.
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DS3 Medium
During an online screening, find the time. What is the time?
Statement ISI is Rs. 3,000.
Statement IIP = Rs. 10,000 and R = 6%.
ExplanationFormula: T = (100 × SI) / (P × R). Statement I alone lacks P and R. Statement II alone lacks SI. Together: T = (100 × 3000) / (10000 × 6) = 5 years. Both are needed. Answer: C. -
DS4 Medium
An HR mock asks a comparison. Is the time greater than 4 years?
Statement IP = Rs. 12,000, SI = Rs. 4,800 and R = 8%.
Statement IIOnly the rate is 8%.
ExplanationFormula: T = (100 × SI) / (P × R). Statement I: T = (100 × 4800) / (12000 × 8) = 5 years, which is greater than 4 years. Statement II alone is insufficient. Answer: A.