The simple interest in $3$ years and compound interest in $2$ years on a certain sum of money at the same rate are $Rs. 1200$ and $Rs. 832$ respectively. The principal is

From the simple interest for 3 years of Rs. 1200, the annual interest is 1200 / 3 = Rs. 400, meaning the interest for 2 years is Rs. 800. Let the principal be P and rate be R, so the compound interest for 2 years is P(1 + R/100)^2 - P = 832. Substituting P(R/100) = 400 gives P(R/100)^2 = 32, so P(R/100)(R/100) = 32 becomes 400(R/100) = 32, yielding R = 8%. Substituting R back, P(0.08) = 400, so the principal is Rs. 5000.

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