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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

1 Answer

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Best 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.

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