A sum of ₹5500 is lent out in two parts in such a way that the interest on one part at 12% for 4 years is equal to that on another part at 8% for 5 years. What will be the two parts of the sum?

₹2500 and ₹3000

The correct answer is Option (3) → ₹2500 and ₹3000

Let the two parts be ₹x and ₹(5500 - x).

Interest on ₹x at 12% for 4 years: $ \text{SI}_1 = \frac{x \times 12 \times 4}{100} = \frac{48x}{100} $

Interest on ₹(5500 - x) at 8% for 5 years: $ \text{SI}_2 = \frac{(5500 - x) \times 8 \times 5}{100} = \frac{40(5500 - x)}{100} $

Given: $ \text{SI}_1 = \text{SI}_2 $

$ \frac{48x}{100} = \frac{40(5500 - x)}{100} $

$ 48x = 40(5500 - x) $

$ 48x = 220000 - 40x $

$ 88x = 220000 $

$ x = \frac{220000}{88} = 2500 $

So, the two parts are:

₹2500 and ₹5500 - ₹2500 = ₹3000

Answer: ₹2500 and ₹3000