Question

A and B divided a sum of rs 84,000 in the ratio 4:3. If rs X is added to each of their shares, the ratio becomes 5:4, then the value of X is:

• A. rs 10,000
• B. rs 12,000
• C. rs 11,000
• D. rs 10,500

Hint:

When the ratio changes after adding an amount to both parts, use the proportion method to find the unknown.

Answer 1

The Correct Option is B

Let the sum of rs 84,000 be divided between A and B in the ratio 4:3. Thus, A's share = \( \frac{4}{7} \times 84000 = 48000 \), and B's share = \( \frac{3}{7} \times 84000 = 36000 \). Let rs X be the amount added to each of their shares. After adding rs X to each, the new shares become \( 48000 + X \) and \( 36000 + X \). The new ratio is given as 5:4, so: \[ \frac{48000 + X}{36000 + X} = \frac{5}{4} \] Cross-multiply to solve for \( X \): \[ 4 \times (48000 + X) = 5 \times (36000 + X) \] \[ 192000 + 4X = 180000 + 5X \] \[ 192000 - 180000 = 5X - 4X \] \[ 12000 = X \] Thus, the value of \( X \) is rs 12,000.