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Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?

  • A.Rs.21.60
  • B.Rs.24.00
  • C.Rs.25.20
  • D.Rs.27.80

Answer: A

He pays simple interest and receives compound interest on the same sum at the same rate, so his profit is the gap between the two.

\[ \text{SI paid} = 6000 \times 0.06 \times 2 = \text{Rs. } 720 \]

\[ \text{CI received} = 6000\left[(1.06)^{2} - 1\right] = 6000(1.1236 - 1) = \text{Rs. } 741.60 \]

\[ \text{income} = 741.60 - 720 = \text{Rs. } 21.60 \]

The shortcut gives it in one line: \( P\left(\tfrac{R}{100}\right)^{2} = 6000 \times 0.0036 = 21.60 \).

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