A certain principal amount at some simple interest becomes Rs 10000 in 2 years, and the same principal amount at the same rate of simple interest becomes Rs 11000 in 3 years. Find the principal and the rate of interest.

ARs 9200 and 14%

BRs 8500 and 13.5%

CRs 9000 and 13%

DRs 8000 and 12.5% ✓ Correct

Correct answer: (D) Rs 8000 and 12.5%

Explanation

The principal is Rs 8000 at 12.5%.

SI for 1 year = amount at 3 years - amount at 2 years = 11000 - 10000 = 1000.

Amount at 2 years = P + 2 years SI, so P = 10000 - 2 x 1000 = 8000.

Rate = (SI per year / P) x 100 = (1000 / 8000) x 100 = 12.5%.

Method: yearly SI from the gap, then back out the principal.

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