A person borrowed some money on simple interest. After 4 years, he returned 9/5 of the money to the lender. What was the rate of interest?

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Let the principal amount be P.

After 4 years, the total amount returned is (9/5)P.

Simple Interest (SI) = Total Amount - Principal = (9/5)P - P = (9/5 - 1)P = (4/5)P.

SI formula: SI = (P × R × T) / 100, where R is rate of interest per annum and T is time in years.

Substitute SI = (4/5)P, T = 4 years:
(4/5)P = (P × R × 4) / 100

Divide both sides by P:
4/5 = (4R) / 100

Multiply both sides by 100:
(4/5) × 100 = 4R

80 = 4R

Divide both sides by 4:
R = 20% per annum.

Therefore, the rate of interest is 20% p.a.

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