Question

In Simple Interest on a sum at 6% per annum for 7 years is equal to twice the Simple Interest on another sum for 9 years at 5% per annum. Find the ratio of the sum invested​

Answer 1

Ratio of the sums is- 284 : 145.

Formula to calculate Simple interest is the product of P(Principal amount) ,N(Number of years),   Rate of Interest (R) divided by 100.

Let us assume the amount to be 'x' and 'y' respectively.

Calculating the interest using the first rate and years,we get R₁ = x * 6* 7 / 100 that is 42x/100

Calculating second interest , R₂ = y * 9 * 5 / 100 that is 45y/100.

Now calculating sums from their interests, S₁ = x + (42x/100) = 142x/100     S₂ = y + 45y/100 = 145y/100

Given is that the rate of interest of first is twice that of the second that is x=2y.

Now taking ratios we get,

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

142x : 145y

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

284 : 145