Sitaram, a money lender lent a part of Rs 200000 to Shyam at simple interest 6% p.a. and the remaining to Sushil at 10% p.a. at simple interest. Sitaram earned an annual interest income of Rs. 18000. Based on the given information answer the following questions :
What is the ratio of the interest paid by Shyam and Sushil respectively
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1:5
Let Shyam borrow Rs P at 6%; Sushil borrows the rest at 10%. The total interest is Rs 18000:
\(0.06P + 0.10(200000 - P) = 18000\)
\(20000 - 0.04P = 18000\)
\(P = 50000\)
So Shyam borrows Rs 50000 and Sushil Rs 150000. Their yearly interest:
\(\text{Shyam: } 0.06 \times 50000 = 3000\)
\(\text{Sushil: } 0.10 \times 150000 = 15000\)
\(3000 : 15000 = 1 : 5\)
Why the other options are incorrect
Option (1) 1:3 — Incorrect. 1 : 3 is the ratio of the amounts borrowed; the interest ratio also depends on the rates 6% and 10%.
Option (3) 3:5 — Incorrect. 3 : 5 is only the ratio of the rates 6% and 10%, ignoring the amounts.
Option (4) 2:3 — Incorrect. The interests are Rs 3000 and Rs 15000, in the ratio 1 : 5.