Select the correct answerA sum of money in 3 years becomes 1344 and in 7 years, becomes Rs. 1536. What is the principal sum where simple rate of interest is to be unchanged?

To solve this problem, we need to use the formula for simple interest which is I = PRT/100, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time in years.

From the problem, we know that the sum of money becomes Rs. 1344 in 3 years and Rs. 1536 in 7 years. This means that the interest earned in 4 years (7 years - 3 years) is Rs. 192 (Rs. 1536 - Rs. 1344).

So, we can set up the equation 192 = P * R * 4 / 100.

We also know that the principal amount plus the interest earned in 3 years is Rs. 1344. So, the interest earned in 3 years is Rs. 1344 - P.

We can set up another equation using the formula for simple interest: 1344 - P = P * R * 3 / 100.

Now we have a system of two equations, and we can solve for P and R. However, the problem asks for the principal sum, so we are only interested in P.

To solve for P, we can multiply the second equation by 4 and subtract the first equation from the result:

4 * (1344 - P) - 192 = P * R * 12 / 100 - P * R * 4 / 100

Solving for P gives us P = Rs. 1200.