A gentleman deposits a portion of his savings in a bank and the remaining in a post office under simple interest. The rates of simple interest in the bank and post office are 10% and 8% respectively. His total savings amount to ₹57,000. If he had deposited the entire amount in the bank, he would have earned ₹500 more in interest. What were the amounts he deposited in the bank and the post office?

Q.A gentleman deposits a portion of his savings in a bank and the remaining in a post office under simple interest. The rates of simple interest in the bank and post office are 10% and 8% respectively. His total savings amount to ₹57,000. If he had deposited the entire amount in the bank, he would have earned ₹500 more in interest. What were the amounts he deposited in the bank and the post office?

Let the gentleman deposit ₹\(x\) in the bank and the remaining ₹\((57000 - x)\) in the post office. At a simple interest rate of 10%, the interest earned from the bank is: \[ \frac{x \times 1 \times 10}{100} = \frac{x}{10} \text{ rupees} \] At a simple interest rate of 8%, the interest earned from the post office is: \[ \frac{(57000 - x) \times 1 \times 8}{100} = \frac{2(57000 - x)}{25} \text{ rupees} \] If he had deposited the entire ₹57000 in the bank, the interest would have been: \[ \frac{57000 \times 1 \times 10}{100} = ₹5700 \] According to the question: \[ \frac{x}{10} + \frac{2(57000 - x)}{25} = 5700 - 500 = 5200 \] Simplifying: \[ \frac{5x + 4(57000 - x)}{50} = 5200 \Rightarrow 5x + 228000 - 4x = 260000 \Rightarrow x = 260000 - 228000 = 32000 \] So, the gentleman deposited ₹32000 in the bank and ₹25000 in the post office.