A part of the sum of ₹31,000 was lent at 9% per annum simple interest and the remaining part at 7% per annum simple interest for a period of 4 years. After 4 years, the total interest received was ₹10,500. Find the ratio of the sum lent at 7% to the sum lent at 9%.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 33 : 91 .
Let amount lent at 9% = x
Then amount lent at 7% = 31000 - x
Simple Interest formula: SI = (P × R × T) / 100
Total interest = 10500
Time = 4 years
So : Interest from 9% = (x × 9 × 4)/100 = 0.36x
Interest from 7% = [(31000 - x) × 7 × 4]/100 = 0.28(31000 - x)
Total interest: 0.36x + 0.28(31000 - x) = 10500
→ 0.36x + 8680 - 0.28x = 10500
→ 0.08x = 1820
→ x = 22750
Amount at 7% = 31000 - 22750 = 8250
Required ratio (7% : 9%) = 8250 : 22750 = 33 : 91