A 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?Options4000120028001500

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 Rs. 1344 in 3 years and Rs. 1536 in 7 years, we can infer that the interest accrued over the 4-year period (from the 3rd year to the 7th year) is Rs. 1536 - Rs. 1344 = Rs. 192.

So, we have I = Rs. 192, T = 4 years. We need to find P (the principal) and we know that the rate of interest R is unchanged.

We can rearrange the simple interest formula to find P: P = I / (RT).

However, we don't have the value for R. But we know that the same sum under the same rate of interest becomes Rs. 1344 in 3 years. So, we can find R from this information.

Let's denote the principal as P1, the total amount after 3 years as A1 = Rs. 1344, and the interest accrued over these 3 years as I1. We have A1 = P1 + I1.

We can express I1 using the simple interest formula: I1 = P1 * R * 3.

Substituting I1 in the equation for A1, we get 1344 = P1 + P1 * R * 3, which simplifies to 1344 = P1 * (1 + 3R).

Now we can express P1 in terms of R: P1 = 1344 / (1 + 3R).

We also know that P1 = I / (RT) = 192 / (4R).

Setting these two expressions for P1 equal to each other, we get 1344 / (1 + 3R) = 192 / (4R).

Solving this equation for R, we get R = 0.04.

Substituting R = 0.04 into the equation for P1, we get P1 = 1344 / (1 + 3*0.04) = Rs. 1200.

So, the principal sum is Rs. 1200.