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 loan
I₁ = 725 × r × 1 ÷ 100 = 7.25r

Step 2: Interest from the second loan
Time 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 equation
I₁ + 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.