​A sum of ₹2600 is lent out at simple interest in two parts. One part at the annual rate of 18 percent and another part at the annual rate of 25 percent. If the total annual interest is ₹520, then what is the sum lent out at the rate of 25 percent per annum?​

Correct option is B

Given:

• Total sum lent = ₹2600
• One part is lent at 18% per annum
• Another part is lent at 25% per annum
• Total interest for 1 year = ₹520
• We need to find the amount lent at 25% rate

Formula Used:

Simple Interest (SI) = (Principal × Rate × Time) / 100

In this case, Time = 1 year, so:

​$$\text{SI} = \frac{\text{Principal} \times \text{Rate}}{100}$$​​

​Solution:​

Let the amount lent at 25% rate be x,
Then the remaining amount at 18% rate = 2600 - x

Interest from amount at 25% = (x × 25) / 100 = 0.25x

Interest from amount at 18% = $$\frac{(2600 - x) \times 18}{100} = 0.18(2600 - x)$$​​

Total interest = ₹520
So:

0.25x + 0.18(2600 - x) = 520

=> 0.25x + 468 - 0.18x = 520
=> (0.25x - 0.18x) = 520 - 468
=> 0.07x = 52
=> x = 52 / 0.07 = ₹742.85

Final Answer: (B) ₹742.85