Question

The interest on a sum of money at 6% p.a. for 7 years is equal to twice the interest on another
sum of money for 9 years at 5% p.a. Find the ratio of the two sums. ​

Answer 1

Ratio of the sums is- 284 : 145.

1. Formula to calculate Simple interest is the product of P(Principal amount) ,N(Number of years),   Rate of Interest (R) divided by 100.
2. Let us assume the amount to be 'x' and 'y' respectively.
3. Calculating the interest using the first rate and years,we get R₁ = x * 6* 7 / 100 that is 42x/100
4. Calculating second interest , R₂ = y * 9 * 5 / 100 that is 45y/100.
5. Now calculating sums from their interests, S₁ = x + (42x/100) = 142x/100     S₂ = y + 45y/100 = 145y/100
6. Given is that the rate of interest of first is twice that of the second that is x=2y.
7. Now taking ratios we get,

(142x/100) / (145y/100)

142x : 145y

142 * 2y : 145y           (As given in step 6)

284 : 145