Single correct option
The difference between the compound interest (compounded annually) and the simple interest on a certain sum for 3 years at 10% per annum is ₹620. The sum is
- A. ₹15,000
- B. ₹20,000
- C. ₹24,000
- D. ₹31,000
Show answer and solution
Answer: (B) ₹20,000
For 3 years at rate r, CI − SI = P[(1 + r)³ − 1 − 3r].
With r = 0.1: (1.1)³ = 1.331, so CI = 0.331P and SI = 0.3P. Difference = 0.031P.
0.031P = 620 ⇒ P = ₹20,000.
Check: CI = 6,620, SI = 6,000, difference 620 ✓.
Shortcut: For 3 years, CI − SI = P·r²(3 + r) = P × 0.01 × 3.1 = 0.031P.
With r = 0.1: (1.1)³ = 1.331, so CI = 0.331P and SI = 0.3P. Difference = 0.031P.
0.031P = 620 ⇒ P = ₹20,000.
Check: CI = 6,620, SI = 6,000, difference 620 ✓.
Shortcut: For 3 years, CI − SI = P·r²(3 + r) = P × 0.01 × 3.1 = 0.031P.
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