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A man received ₹ 1520 for selling a table and chair together, earning a profit of 10% on the table and 25% on the chair. He would have made a profit of 10% on the chair and 25% on the table if he had sold them for ₹ 1535. What will be the chair’s and table’s cost price?

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₹ 600 and ₹ 700

₹ 700 and ₹ 600

₹ 600 and ₹ 600

₹ 700 and ₹ 700

answer is A.

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Detailed Solution

It is given that a man sold a table and chair together for ₹ 1520 making a profit of 10% on the table and 25% on the chair.
Let’s assume that the cost of the chair is

x

and the cost of a table is

y .

According to the question, we have,

x + 25 x 100 + y + 10 y 100 = 1520 ⇒ 25 x + 22 y = 30400 ​ ​ (1)

It is also given that he makes a profit of 10% on the chair and 25% on the table if he had sold them for ₹ 1535.
Therefore we have,

x + 10 x 100 + y + 25 y 100 = 1535 ⇒ 22 x + 25 y = 30700 (2)

Multiplying equation (1) by 22 and equation (2) by 25, we get,

550 x + 484 y = 668800 ​ ​ (3) 550 x + 625 y = 767500 (4) ​

Subtracting equation (3) from equation (4), we get,

y = 700

∵ 25 x + 22 y = 30400 ⇒ 25 x + 22 × 700 = 30400 ⇒ x = 600

Therefore the chair’s and table’s cost prices are respectively ₹ 600 and ₹ 700.
Hence option (1) is correct.

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