A person purchased a table and a sofa for ₹28,000. He sold the sofa at a profit of 10% and the table at a profit 15.25%. If his total profit was 13%, then the difference between the cost price of the sofa and the table (in ₹) is:

Correct — B. Sofa and table cost ₹28,000 together. Profit rates: sofa 10%, table 15.25%, overall 13%.

Apply alligation to the rates:
sofa : table = (15.25 − 13) : (13 − 10)
= 2.25 : 3 = 3 : 4

Split ₹28,000 in 3 : 4:
sofa = 28000 × 3⁄7 = ₹12,000
table = 28000 × 4⁄7 = ₹16,000

Difference = 16000 − 12000 = ₹4,000 → option (b)

Check: 10% of 12,000 plus 15.25% of 16,000 = 1,200 + 2,440 = ₹3,640, which is exactly 13% of ₹28,000.

Why the others are wrong

• (a)
  5000 — A gap of ₹5,000 means costs of ₹11,500 and ₹16,500. Those earn 1,150 + 2,516.25 = ₹3,666.25, a return of 13.09% — above the 13% the stem fixes, because too much cost sits on the higher-margin table.
• (c)
  2500 — ₹2,500 puts the costs at ₹12,750 and ₹15,250, earning ₹3,600.625 in all, or 12.86%. Shifting cost onto the sofa, the lower-margin item, drags the overall rate under 13%.
• (d)
  1500 — ₹1,500 gives ₹13,250 and ₹14,750 and a return of ₹3,574.375, which is 12.77%. The narrower the gap, the closer the overall rate slides to the plain midpoint of 10% and 15.25%, namely 12.625%.

This is alligation applied to profit rates, not to prices. The overall 13% is a weighted average of 10% and 15.25%, and the weights are the two cost prices.

The rule crosses over: the distance from the mean to one rate becomes the weight of the other item.

sofa : table = (15.25 − 13) : (13 − 10) = 2.25 : 3 = 3 : 4

Because 13% sits closer to 15.25% than to 10%, the table — the higher-margin item — must carry the larger share of the ₹28,000. The weights attach to costs, which is why the answer is a difference in rupees rather than in per cent.

Key facts

• The alligation ratio is (15.25 − 13) : (13 − 10) = 2.25 : 3 = 3 : 4, sofa to table.
• Sofa cost ₹12,000 and table cost ₹16,000, summing to the ₹28,000 given.
• Total profit is ₹3,640, which is 13% of ₹28,000.
• Alligation weights attach to cost prices, so 3 : 4 splits the ₹28,000 and not the profit.

Common traps

• Pairing each rate with its own distance from the mean instead of crossing them over.
• Assuming the table is the cheaper item because it is named first.
• Treating 3 : 4 as the split of the profit rather than of the ₹28,000 cost.

No directly related past PYQ was found.