The simple interest on a certain sum for 3 years at 8% per annum is ₹96 more than the simple interest on the same sum for 2 years at 9% per annum. Find the sum.

Correct option is B

Given:

Simple interest for 3 years at 8% per annum = ₹96 more than

Simple interest for 2 years at 9% per annum

Time and rate differ, principal is same

Formula Used:

Use the simple interest formula:

SI = $$\frac{P \times R \times T}{100}$$​​

Solution:

Let the sum be ₹P

Now,

​$$\frac{P \times 8 \times 3}{100} - \frac{P \times 9 \times 2}{100} = 96 \\ \ \\\frac{24P}{100} - \frac{18P}{100} = 96 \\ \ \\ \frac{6P}{100} = 96 \\ \ \\ P = \frac{96 \times 100}{6} = 1600$$ ​