Multiple choice

A young entrepreneur takes a loan of Rs. 1,50,000 from a bank for a period of 6 years to expand his retail store. He borrows part of the amount at an interest rate of 4% per annum under a government-supported loan for small businesses, and the remaining part at 7% per annum under a standard commercial loan. The total interest he has to pay at the end of 6 years is Rs. 41,400. What is the ratio of the loan amount borrowed under the government-supported loan for small businesses to the amount borrowed under the commercial loan?

  1. 2 : 3

  2. 1 : 4

  3. 3 : 2

  4. 4 : 1

  5. 5 : 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total interest for 6 years is 41,400 rupees, which means the interest per year is 6,900 rupees. Let x be the amount borrowed at 4% and (1,50,000 - x) be the amount at 7%. Solving the annual interest equation 0.04x + 0.07(1,50,000 - x) = 6,900 gives x = 1,20,000 rupees, meaning the remaining commercial loan is 30,000 rupees. The ratio of the two amounts is 1,20,000 : 30,000, which simplifies to 4 : 1.

AI explanation

Let the amount borrowed under the government-supported loan be x, making the commercial loan amount 150000 - x. The total interest equation is 6 * 4 * x / 100 + 6 * 7 * (150000 - x) / 100 = 41400. This simplifies to 24x + 6300000 - 42x = 690000, which means 18x = 540000, so x = 30000. The commercial loan amount is 150000 - 30000 = 120000. The required ratio of the government-supported loan to the commercial loan is 30000 : 120000, which simplifies to 4 : 1.

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