A sum of Rs. 1,550 was lent partly at 5% and partly at 8% per annum simple…
2024
A sum of Rs. 1,550 was lent partly at 5% and partly at 8% per annum simple interest. The total interest received after 3 years was Rs. 300. The ratio of money lent at 5% to that lent at 8% is:
- A.
5 : 8
- B.
8 : 5
- C.
31 : 6
- D.
16 : 15
Show answer & explanation
Correct answer: D
Concept: When a sum is split into two parts and lent at different simple-interest rates, the total interest earned is the sum of the interest from each part, Simple Interest = (Principal × Rate × Time) / 100 applied separately to each part and added together. This gives one linear equation in the unknown split, which is solved to find the two principal amounts.
Let the amount lent at 5% be x. Then the amount lent at 8% is (1550 − x).
The interest earned per year is (x × 5)/100 from the first part and ((1550 − x) × 8)/100 from the second part.
Over 3 years, the total interest is 3 × [0.05x + 0.08(1550 − x)] = 300.
Simplifying: 0.05x + 124 − 0.08x = 100, so −0.03x = −24.
Solving gives x = 800, so the amount at 5% is Rs. 800 and the amount at 8% is 1550 − 800 = Rs. 750.
The ratio of the two amounts is 800 : 750, which simplifies to 16 : 15.
Cross-check: Interest from Rs. 800 at 5% for 3 years = (800 × 5 × 3)/100 = Rs. 120. Interest from Rs. 750 at 8% for 3 years = (750 × 8 × 3)/100 = Rs. 180. Total = 120 + 180 = Rs. 300, which matches the given total interest, confirming the split is correct.