A sum of ₹ 22,100 was divided between Timir and Monali in such a way that if both invested their shares at 10% compound interest per annum, the amount payable on maturity to Monali after 18 years would be the same as the amount payable on maturity to Timir after 20 years. What was the share of Monali in the initial sum?

Correct option is D

Given:

- Total sum = ₹ 22,100

- Rate of interest (r) = 10% per annum

- Monali’s time (t₁) = 18 years

- Timir’s time (t₂) = 20 years

- Let Monali’s share = ₹ M

- Let Timir’s share = ₹ T = 22,100 – M

Formula Used:

Amount, A = $$P × (1 +\frac{ r}{100}) ^ t$$​​

Solution:

Amount for Monali = Amount for Timir

​$$\begin{aligned}&M \times \left(1 + \frac{10}{100}\right)^{18} = T \times \left(1 + \frac{10}{100}\right)^{20} \\\ \\&M \times (1.1)^{18} = (22,100 - M) \times (1.1)^{20} \\\ \\&M = (22,100 - M) \times (1.1)^2 \\\ \\&M = (22,100 - M) \times 1.21 \\\ \\&M = 22,100 \times 1.21 - 1.21 \times M \\\ \\&M + 1.21 \times M = 22,100 \times 1.21 \\\ \\&2.21 \times M = 22,100 \times 1.21 \\\ \\&M = \frac{22,100 \times 1.21}{2.21} \\\ \\&M \approx \text{₹ } 12,100\end{aligned}$$​​

The share of Monali in the initial sum was approximately ₹ 12,100.