Difference in profit shares from ratio – UGC NET Question

If A and B share profits in the ratio 7:9, the total number of parts is 7 + 9 = 16. Each part is worth ₹1,60,000 ÷ 16 = ₹10,000. A’s share is 7 × ₹10,000 = ₹70,000 and B’s share is 9 × ₹10,000 = ₹90,000. The difference between their shares is ₹90,000 − ₹70,000 = ₹20,000.

Option A:
Option A is correct because it directly reflects the difference between 7 parts and 9 parts when each part is ₹10,000. The arithmetic shows that the financial gap between A and B is exactly two parts, which equals ₹20,000. This fits both the total profit and the specified sharing ratio.

Option B:
Option B, ₹22,000, would not correspond to an integer number of ratio parts, given that each part is ₹10,000. It would imply a difference of 2.2 parts, which contradicts the whole-number nature of the ratio 7:9 and the discrete sharing of profit.

Option C:
Option C, ₹24,000, would amount to a difference of 2.4 parts, which again is inconsistent with the ratio 7:9. Using this figure would mean the implied total profit cannot be exactly ₹1,60,000 when aligned with the ratio.

Option D:
Option D, ₹25,000, suggests an even more irregular difference and would break the connection between the ratio parts and the fixed total profit. When we reverse-calculate, no whole-number ratio 7:9 with a total of 16 parts yields a difference of ₹25,000, so this option is impossible under the given conditions.