Two friends A and B jointly lent out Rs 81600 at 4% compound interest.

1.	Two friends A and B jointly lent out Rs 81600 at 4% compound interest. After 2 years A gets the same amount as B gets after 3 years. The investment made by B was (a) Rs 40000 (b) Rs 30000 (c) Rs 45000 (d) Rs 38000
Answer» (a) Rs 40000 Let the investment made by A be Rs x. Then, investment made by B = Rs (81600 – x) Given, x\(\big(1+\frac{4}{100}\big)^2\) = (81600-x)\(\big(1+\frac{4}{100}\big)^3\) \(\Rightarrow\)\(\frac{X}{(81600-X)}\) = \(\frac{\big(1+\frac{4}{100}\big)^3}{\big(1+\frac{4}{100}\big)^2}\) \(\Rightarrow\) \(\frac{X}{(81600-X)}\) - \(\big(1+\frac{4}{100}\big)\) - \(\frac{26}{25}\) \(\Rightarrow\) 25x = (81600 – x) × 26 \(\Rightarrow\) 25x + 26x = 81600 × 26 \(\Rightarrow\) 51x = 81600 × 26 \(\Rightarrow\) x = \(\frac{81600\times26}{51}\) = 41600 \(\therefore\) Investment made by B = Rs (81600 – Rs 41600) = Rs 40000.

Two friends A and B jointly lent out Rs 81600 at 4% compound interest. After 2 years A gets the same amount as B gets after 3 years. The investment made by B was (a) Rs 40000 (b) Rs 30000 (c) Rs 45000 (d) Rs 38000

Answer»

(a) Rs 40000

Let the investment made by A be Rs x. Then,

investment made by B = Rs (81600 – x)

Given, x\(\big(1+\frac{4}{100}\big)^2\) = (81600-x)\(\big(1+\frac{4}{100}\big)^3\)

\(\Rightarrow\)\(\frac{X}{(81600-X)}\) = \(\frac{\big(1+\frac{4}{100}\big)^3}{\big(1+\frac{4}{100}\big)^2}\)

\(\Rightarrow\) \(\frac{X}{(81600-X)}\) - \(\big(1+\frac{4}{100}\big)\) - \(\frac{26}{25}\)

\(\Rightarrow\) 25x = (81600 – x) × 26

\(\Rightarrow\) 25x + 26x = 81600 × 26

\(\Rightarrow\) 51x = 81600 × 26

\(\Rightarrow\) x = \(\frac{81600\times26}{51}\) = 41600

\(\therefore\) Investment made by B = Rs (81600 – Rs 41600)

= Rs 40000.