Mr. James invested an amount A in one bank account at 25% p.a. simple interest and ₹(A + 1,000) in another bank account at 50% p.a., compounded semi-annually. After one year, the amount received from the second account was ₹3,750 more than the amount received from the first account. Find the value of A.

The amount from the first account after one year is A plus (A multiplied by 25 divided by 100), which equals 1.25A. The amount from the second account is compounded semi-annually at 50% (effective rate 25% per half-year), giving an amount of (A + 1000) multiplied by 1.5625. Since the second amount is 3750 more than the first, 1.5625A + 1562.5 - 3750 equals 1.25A, which solves to 0.3125A = 2187.5, making A equal to 7000.

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