A sum of money in 3 years becomes 1344 and in 7 years it 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 a sum of money becomes Rs. 1344 in 3 years and Rs. 1536 in 7 years. This means that the interest accrued over 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 interest accrued over the first 3 years is Rs. 1344 - P.

So, we can set up another equation 1344 - P = P * R * 3 / 100.

Now we have a system of two equations, and we can solve for P and R.

First, let's solve the first equation for R: R = 192 * 100 / (P * 4).

Then, substitute R in the second equation: 1344 - P = P * (192 * 100 / (P * 4)) * 3 / 100.

Solving this equation for P gives us the principal amount.