Question

Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

• A. 20920
• B. 20930
• C. 20950
• D. 209700

Answer 1

The Correct Option is A

Let the amount invested by Bimal be ₹P.

Interest Earned by Amal:

• Amal invests ₹12,000 at 8% simple interest for 1 year.
• So, his amount after 1 year: \[ A_1 = 12000 \left(1 + \frac{8}{100}\right) = 12000 \times 1.08 = ₹12,960 \] Interest earned: \[ I_1 = 12960 - 12000 = ₹960 \]
• Amal also invests ₹10,000 at 3% compound interest for 2 years.
• Amount after 2 years: \[ A_2 = 10000 \left(1 + \frac{3}{100}\right)^2 = 10000 \times 1.0609 = ₹10,609 \] Interest earned: \[ I_2 = 10609 - 10000 = ₹609 \]

Total Interest Earned by Amal:

\[ I_{\text{Amal}} = I_1 + I_2 = 960 + 609 = ₹1,569 \]

Interest Earned by Bimal:

Bimal invests ₹P at 7.5% simple interest for 1 year.

\[ I_{\text{Bimal}} = P \times \frac{7.5}{100} \]

Equating the Interests:

\[ P \times \frac{7.5}{100} = 1569 \] \[ P = \frac{1569 \times 100}{7.5} = ₹20920 \]

Final Answer: The amount invested by Bimal is \( \boxed{₹20920} \).