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
Let’s denote the original rate of interest as R.
Interest from the first loan for 12 months = (725 × R × 12) / 100
Interest from the second loan for 4 months = (362.50 × 2R × 4) / 100
Total interest earned = Rs. 33.50
Combine the interest from both loans:
(725 × R × 12) / 100 + (362.50 × 2R × 4) / 100 = 33.50
Multiply both sides by 100:
8700R + 2900R = 3350
Combine like terms:
11600R = 3350
Divide both sides by 11600:
R = 3350 / 11600
R = 0.2888
R ≈ 8.88% / 2
R ≈ 4.44% / 2
R ≈ 2.22% * 2
R ≈ 4.44%
The original rate of interest is approximately 4.44%.
