Practice Questions
Concept Explanation
When simple interest, rate, and time are known, rearrange the SI formula to find the principal.
Key Formula
P = (100 × SI) / (R × T)
Alternatively, if amount (A) is known: P = A − SI or P = 100A / (100 + RT)
Example
SI = Rs. 900 at 6% for 5 years. P = (100 × 900)/(6 × 5) = Rs. 3,000.
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Q1 EasyA sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:ExplanationUnder simple interest, the interest earned each year is constant. SI for 1 year = 854 − 815 = Rs. 39. SI for 3 years = 39 × 3 = Rs. 117. Principal = Amount after 3 years − SI for 3 years = 815 − 117 = Rs. 698. Hence the answer is Rs. 698.
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Q2 EasyA man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:ExplanationFormula: P = (100 × SI) / (R × T). P = (100 × 5400) / (12 × 3) = 540000 / 36 = Rs. 15,000. Hence the principal is Rs. 15,000.
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Q3 EasySI is Rs. 1,200 at 8% for 3 years. The principal is:ExplanationFormula: P = (100 × SI) / (R × T). P = (100 × 1200) / (8 × 3) = 120000 / 24 = Rs. 5,000. Hence the answer is Rs. 5,000.
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Q4 EasyAt 5% for 5 years, SI is Rs. 750. Principal is:ExplanationFormula: P = (100 × SI) / (R × T). P = (100 × 750) / (5 × 5) = 75000 / 25 = Rs. 3,000. Hence the answer is Rs. 3,000.
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Q5 EasyAmount is Rs. 5,600 and SI is Rs. 600. Principal is:ExplanationFormula: Principal = Amount − SI. P = 5600 − 600 = Rs. 5,000. Hence the answer is Rs. 5,000.
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Q6 MediumA sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?ExplanationFormula: P = (100 × SI) / (R × T). P = (100 × 4016.25) / (9 × 5) = 401625 / 45 = Rs. 8,925. Hence the answer is Rs. 8,925.
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Q7 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 sum 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. Hence the answer is Rs. 6,125.
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Q8 MediumSI = Rs. 2,400 at 12% for 2 years. Find the principal.ExplanationFormula: P = (100 × SI) / (R × T). P = (100 × 2400) / (12 × 2) = 240000 / 24 = Rs. 10,000. Hence the answer is Rs. 10,000.
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Q9 MediumIn a placement drill, SI = Rs. 1,620 at 6% for 3 years. Principal is:ExplanationFormula: P = (100 × SI) / (R × T). P = (100 × 1620) / (6 × 3) = 162000 / 18 = Rs. 9,000. Hence the answer is Rs. 9,000.
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Q10 HardA sum of money becomes Rs. 20952 after 2 years and Rs. 24444 after 3 years when lent at compound interest. Principal is:ExplanationInterest for the 3rd year = 24444 − 20952 = Rs. 3,492. This interest is earned on the amount after 2 years, so R = (3492 / 20952) × 100 = (1/6) × 100 = 16⅔%. Formula: A = P(1 + R/100)^n ⇒ 20952 = P(7/6)^2 ⇒ P = 20952 × 36/49 = 754272/49 ≈ Rs. 15,393. Hence the principal is Rs. 15,393.
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Q11 HardSimple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:ExplanationCI on Rs. 4000 for 2 years at 10% = 4000[(1.1)^2 − 1] = 4000(1.21 − 1) = 4000 × 0.21 = Rs. 840. Half of CI = 840 / 2 = Rs. 420 = SI. Formula: P = (100 × SI) / (R × T) = (100 × 420) / (8 × 3) = 42000 / 24 = Rs. 1,750. Hence the sum is Rs. 1,750.
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Q12 HardA certain sum of money amounts to Rs. 1008 in 2 years and to Rs. 1164 in 3 1/2 years. Find the sum and rate of interest.ExplanationSI for (3½ − 2) = 1½ years = 1164 − 1008 = Rs. 156. SI for 1 year = 156 / 1.5 = Rs. 104. SI for 2 years = 104 × 2 = Rs. 208. Principal = 1008 − 208 = Rs. 800. Rate R = (100 × SI) / (P × T) = (100 × 104) / (800 × 1) = 13%. Hence the sum is Rs. 800 and the rate is 13%.
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Q13 HardSI = Rs. 880 at 8% for 2.5 years. Principal is:ExplanationFormula: P = (100 × SI) / (R × T). P = (100 × 880) / (8 × 2.5) = 88000 / 20 = Rs. 4,400. Hence the answer is Rs. 4,400.
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Q14 HardAmount is Rs. 6,960 at 8% simple interest for 2 years. Principal is:ExplanationFormula: P = 100A / (100 + RT). Here RT = 8 × 2 = 16. P = (100 × 6960) / (100 + 16) = 696000 / 116 = Rs. 6,000. Verification: SI = (6000 × 8 × 2)/100 = Rs. 960 and Amount = 6000 + 960 = Rs. 6,960. Hence the answer is Rs. 6,000.
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DS1 Easy
What is the principal?
Statement ISimple interest is Rs. 1,200 at 8% per annum for 3 years.
Statement IIThe rate of interest is 8% per annum only (SI and time not given).
ExplanationFormula: P = (100 × SI) / (R × T). Statement I alone: P = (100 × 1200) / (8 × 3) = Rs. 5,000. Statement II alone is insufficient. Answer: A. -
DS2 Easy
During an online screening test, find the principal. What is the principal?
Statement ISimple interest is Rs. 900.
Statement IIRate is 6% per annum and time is 5 years.
ExplanationFormula: P = (100 × SI) / (R × T). Statement I alone lacks R and T. Statement II alone lacks SI. Together: P = (100 × 900) / (6 × 5) = Rs. 3,000. Both are needed. Answer: C.
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DS3 Medium
A placement bank worksheet asks for the invested sum. What is the principal?
Statement IThe amount after 5 years is Rs. 3,750.
Statement IIRate is 5% per annum and time is 5 years.
ExplanationFormula: P = 100A / (100 + RT). Statement I alone lacks R (and uses A only). Statement II alone lacks A. Together: RT = 25, so P = (100 × 3750) / 125 = Rs. 3,000. Both are needed. Answer: C. -
DS4 Medium
An HR mock asks a comparison question. Is the principal greater than Rs. 5,000?
Statement ISI is Rs. 1,800 at 9% per annum for 4 years.
Statement IIOnly the rate is 9% per annum.
ExplanationFormula: P = (100 × SI) / (R × T). Statement I: P = (100 × 1800) / (9 × 4) = Rs. 5,000, which is not greater than Rs. 5,000, so the answer is No. Statement II alone is insufficient. Answer: A.