Question

Divide Rs. 1301 between A and B, so that amount of A after 7 years is equal to the amount of B after 9 years at 4% per annum compounded annually. What was the sum of A and B initially?
1. Rs. 255 and Rs. 356
2. Rs. 426 and Rs. 455
3. Rs. 365 and Rs. 305
4. Rs. 281 and Rs. 260
5. Rs. 676 and Rs. 625

Answer 1

Correct Answer - Option 5 : Rs. 676 and Rs. 625

Given:

Total sum = Rs. 1301

Amount of A after 7 years = Amount of B after 9 years

Rate of Interest = 4% per annum

Concept Used:

C.I = P [{1 + (R/100)}ⁿ - 1]

R = Rate of Interest

T = Time

Calculation:

Let the sum of A and B be Rs. x and Rs. (1301 - x) respectively.

⇒ x{1 + (4/100)}⁷= (1301 - x){1 + (4/100)}9

⇒ x/(1301 - x) = {1 + (4/100)}²

⇒ x/(1301 - x) = (26/25)²

⇒ 625x = 676(1301 - x)

⇒ 1301x = 676 × 1301

Sum of A = x = 676.

Sum of B = (1301 - x) = 1301 - 676

⇒ Sum of B = 625.

∴ The sum of A and B initially was Rs. 676 and Rs. 625.