Select the correct answerA 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?Options24000360006300012000

The problem is about simple interest. The formula for simple interest is I = PRT, where I is the interest, P is the principal, R is the rate, and T is the time.

Given that a sum of money becomes 1344 in 3 years and 1536 in 7 years, we can infer that the interest accrued over the 4-year difference (7 years - 3 years) is 1536 - 1344 = 192.

So, we have I = 192, T = 4, and we need to find P (the principal). We also know that the rate of interest is unchanged, which means we can use the interest from the first 3 years to find the rate.

First, let's find the interest for the first 3 years: 1344 - P. We don't know P yet, but we can express the interest in terms of P.

Now, we can set up the equation for the simple interest for the first 3 years:

1344 - P = P * R * 3

And the equation for the 4-year difference:

192 = P * R * 4

We can divide the second equation by the first to eliminate R:

(192 / 4) / ((1344 - P) / 3) = P

48 / ((1344 - P) / 3) = P

Solving this equation for P gives P = 12000. So, the principal sum is Rs. 12000.