A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

Given data

• Loan 1: Rs. 725 for the whole year at r% p.a.
• Loan 2: After 8 months, lend Rs. 362.50 for the remaining 4 months at twice the former rate = 2r% p.a.
• Total interest earned in the year = Rs. 33.50

Step 1: Interest from the first loanI₁ = 725 × r × 1 ÷ 100 = 7.25r

Step 2: Interest from the second loanTime for second loan = 4 months = 4/12 yearsI₂ = 362.50 × (2r) × (4/12) ÷ 100= 362.50 × 2r × 1/3 ÷ 100= (725/3) × r ÷ 100 = (7.25/3)r

Step 3: Total interest equationI₁ + I₂ = 7.25r + (7.25/3)r = (29/3)r(29/3)r = 33.50r = 33.50 × (3/29) = 3.465517241... % p.a.≈ 3.47% p.a.

Final Answer: Original rate of interest = 3.47% per annum.