Question

A person lent out some money for 1 year at 6% per annum simple interest and after 18 months, he again lent out the same money at a simple interest of 24% per annum. In both the cases, he got Rs 4704. Which of these could be the amount that was lent out in each case if interest is paid half-yearly?

• A. Rs 4000
• B. Rs 4400
• C. Rs 4200
• D. Rs 3600

Answer 1

The correct option is C Rs 4200

We have P same for both the cases.
Let t = number of half- years for 1st case, then number of half-years for second case (as it was lend after 18 months)
$\therefore \frac{P\times 3\times t}{100}=\frac{P\times 3\times (t-3)}{100}$
Solving we get, t = 4.
Hence, $P+\frac{P\times 3\times 4}{100}=4704$
P = 4200

Alternatively:
In the first case, the rate of interest is 3% per half-year. The money will become

1.03x after 6 months from t = 0

1.06x after 12 months from t = 0

1.09x after 18 months from t = 0

1.12x after 24 months from t = 0 and so on ….

In the second case, the rate of interest is 12% per half-year. The money is given out at t = 18.

The money will become:

1.12x after 6 months from t = 18, which is 24 months from t = 0.

So after 2 years, the returns from both the investments will be same. They will be 1.12x
This was the point at which he gets back 4704 Rs.

=> 1.12x = 4704

=> x = 4200 Rs.