Question: Swarn, an SME enterprise, borrowed a sum of money from a nationalised bank at 10% simple interest per annum and the same amount at 8% simple interest per annum from a microfinance firm for the same period. It cleared the first loan 6 months before the scheduled date of repayment and repaid the second loan just at the end of scheduled period. If, in each case, it had to pay Rs. 62,100 as amount, then how much money and for what time period did it borrow?

Explanation:

Let the amount borrowed from each source be Rs. P for n months.

Since Swarn pays Rs. 62,100 to each firm, it pays the same simple interest to each firm.

Since it repays the bank 6 months before repayment, its effective loan tenure is (n − 6) months; while for the loan with the microfinance firm, its tenure is n months.

Considering same interest: [P × 10 × (n − 6)]/(12 × 100) = [P × 8 × n]/(12 × 100)

∴ 5(n − 6) = 4n i.e. n = 30

Hence, time period of borrowing = 30 months = 2.5 years. Hence, options 1 and 2 are eliminated.

Considering the loan with the microfinance firm:

62100 − P = (P × 8 × 2.5)/100

∴ 62100 = 1.2P i.e. P = Rs. 51,750

Hence, option (c).

Alternatively,

Consider the loan with the microfinance firm. Let the amount borrowed be Rs. P for n years.

∴ 62100 − P = (P × 8 × n)/100

∴ 62100 = P(1 + 0.08n)

Now, observe that there are only two values of n (2 and 2.5) in the options). Substitute each value in the above equation and check if the Principal value given in that option is obtained.

When n = 2; P = 62100/1.16 = Rs. 53,535 (approximately). SInce this value is not in the options, this case is invalid.

When n = 2.5; P = 62100/1.2 = Rs. 51,750

Hence, option (c).