Question

‘A’ borrowed money at 4% per annum simple interest payable yearly and lent it immediately at 6% per annum compound interest payable half-yearly and gained thereby 209 rupees at the end of a year. What sum of money did he borrow?

• A. 10,000
• B. 1000
• C. 20,000
• D. None of these

Answer 1

The correct option is A 10,000

Let amount borrowed be Rs. X

Amount to be paid back = Rs. 1.04X

Amount received due to lending at 6% compound interest payable half -yearly = $x(1+\frac{6}{200}{)}^2=1.0609x$

Profit = 1.0609X – 1.04X = 209

0.0209X = 209, X = 10,000; ‘A’ borrowed Rs.10, 000 initially. Option(a)

Alternate Solution

We see that the answer options are far apart and hence the exact calculations are not required. There is an increase of 2% and he is gaining 209 rupees in one year.Hence the amount has to be close to 10000 and hence the answer.