If the compound interest on a certain sum at 16⅔% per annum for 3 years is ₹1,270, find the simple interest on the same sum at th…

Question

If the compound interest on a certain sum at 16⅔% per annum for 3 years is ₹1,270, find the simple interest on the same sum at the same rate and for the same period.

1. A. ₹1,080 (Correct answer)
2. B. ₹1,000
3. C. ₹1,500
4. D. ₹2,000

Correct Answer

Option A — ₹1,080

Detailed Solution & Explanation

The correct answer is ₹1,080.

Key Points

• Convert the rate to a fraction: 16⅔% = 1/6, so each year multiplies the sum by 7/6.
• Over three years: A = P(7/6)³ = P × 343/216, so CI = P(343 − 216)/216 = 127P/216.
• Setting 127P/216 = 1,270 gives P = 1,270 × 216/127 = 10 × 216 = ₹2,160.
• Simple interest = P × R × T/100 = 2,160 × (1/6) × 3 = ₹1,080.

Additional Information

• Awkward-looking rates are usually clean fractions: 16⅔% = 1/6, 12½% = 1/8, 33⅓% = 1/3, 8⅓% = 1/12, 6¼% = 1/16 — converting first removes nearly all the arithmetic.
• CI always exceeds SI over more than one period; here the difference is 1,270 − 1,080 = ₹190, the interest earned on previously accumulated interest.
• For two years the difference between CI and SI is exactly PR²/10⁴, a result asked in its own right.

प्रश्न (हिन्दी में)

यदि किसी निश्चित धनराशि पर 16⅔% प्रति वर्ष की दर से 3 वर्षों का चक्रवृद्धि ब्याज ₹1,270 है, तो उसी धनराशि पर समान दर से और समान अवधि के लिए साधारण ब्याज ज्ञात कीजिए।

1. A. ₹1,080
2. B. ₹1,000
3. C. ₹1,500
4. D. ₹2,000