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 of 15.25%. If his total profit was 13%, then what is the difference between the cost price of the sofa and the table (in ₹)?

Question

Accepted Answer

Let the cost price of the sofa be x and the cost price of the table be (28000 - x).

Profit on sofa = 10% of x = 0.10x
Profit on table = 15.25% of (28000 - x) = 0.1525(28000 - x)

Total profit = 13% of 28000 = 0.13 × 28000 = 3640

According to the problem:
0.10x + 0.1525(28000 - x) = 3640

Expanding:
0.10x + 0.1525 × 28000 - 0.1525x = 3640
0.10x + 4270 - 0.1525x = 3640

Combine like terms:
(0.10 - 0.1525)x + 4270 = 3640
-0.0525x = 3640 - 4270
-0.0525x = -630

Divide both sides by -0.0525:
x = -630 / -0.0525 = 12000

So, cost price of sofa = ₹12,000
Cost price of table = 28000 - 12000 = ₹16,000

Difference = 16000 - 12000 = ₹5000

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