Question

a certain sum invested on simple interest. the amount to which it had grown in 5 years was 5/4 times the amount to which it had grown in 3 years. the percentage rate of interest was​

Answer 1

Dear Student,

◆ Answer -

Rate of interest = 20 %

● Explanation -

Let P be the sum invested at interest rate r.

In 3 years,

x = P (1 + r×t)

x = P (100 + r×3)

x = P (1 + 3r) ...(1)

In 5 years,

x = P (1 + r×t)

5x/4 = P (1 + r×5)

x = 4P/5 (1 + 5r) ...(2)

From (1) & (2),

P (1 + 3r) = 4P/5 (1 + 5r)

1 + 3r = 4/5 (1 + 5r)

1 + 3r = 4/5 + 4r

4r - 3r = 1 - 4/5

r = 1/5

r = 1/5 × 100%

r = 20 %

Hence, the percentage rate of interest was 20 %.

Thanks dear. Hope this helps you...