(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.