If the simple interest on a sum of money at 6% p.a for 7 years is equal to twice the simple interest on another sum for 9 years at 5% p.a, the ratio of the principal amounts will be

Using the simple interest formula, the first condition gives (P1 x 6 x 7) divided by 100, which is 0.42 times P1. The second condition gives (P2 x 5 x 9) divided by 100, which is 0.45 times P2. Equating the first interest to twice the second interest gives 0.42 P1 equals 0.90 P2, so P1 divided by P2 equals 0.90 divided by 0.42. Simplifying this ratio by dividing both sides by 0.06 yields 15 divided by 7, meaning the ratio is 15 : 7.

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