Mr. Shiva invested equal amount of money in two private firms which gives 15%…
2017
Mr. Shiva invested equal amount of money in two private firms which gives 15% simple interest per annum for 3.5 years and 5 years respectively. If the difference in their interests is Rs. 270, the amount invested by Mr. Shiva is:
Answer: B. Rs. 1200 — ConceptSimple Interest depends only on the principal, the rate, and the time: SI = (P × R × T) / 100. When the same principal is lent at the same rate for two…
- A.
Rs. 1500
- B.
Rs. 1200
- C.
Rs. 1250
- D.
Rs. 1205
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Show answer & explanation
Correct answer: B
Concept
Simple Interest depends only on the principal, the rate, and the time: SI = (P × R × T) / 100. When the same principal is lent at the same rate for two different periods, the two interests differ only because the times differ, so the difference equals (P × R × (T2 − T1)) / 100. This relationship lets you recover the principal from a known gap between the two interests.
Application
Let the amount placed in each firm be Rs. x, with rate R = 15% per annum and times T1 = 3.5 years and T2 = 5 years.
Interest for 5 years = (x × 15 × 5) / 100 = 75x / 100.
Interest for 3.5 years = (x × 15 × 3.5) / 100 = 52.5x / 100.
Difference of the two interests = 75x / 100 − 52.5x / 100 = 22.5x / 100, and this equals the given 270.
Solve 22.5x / 100 = 270, so 22.5x = 27000, giving x = 1200.
Cross-check
Use the gap formula directly: difference = (P × R × (T2 − T1)) / 100 = (1200 × 15 × 1.5) / 100 = 27000 / 100 = 270, which matches the given difference. So the amount invested in each firm is Rs. 1200.