Question

A man sold a chair and a table together for Rs. 1520, thereby making a profit of 25% on chair and 10% on table. By selling them together for Rs. 1535, he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.

Answer 1

Let the cost price of the chair and table be Rs. x and Rs. y respectively.

Then as per the question

Selling price of chair + Selling price of table = 1520

`(100 + 25)/100 xx x + (100 + 10)/100 xx y = 1520`

⇒ `125/100 x + 110/100 y = 1520`

⇒ 25x + 22y – 30400 = 0   ...(i)

When the profit on chair and table are 10% and 25% respectively, then

`(100 + 10)/100 xx x + (100 + 25)/100 xx y = 1535`

⇒ `110/100 x + 125/100 y = 1535`

⇒ 22x + 25y – 30700 = 0   ...(ii)

Solving (i) and (ii) by cross multiplication, we get

`x/((22)(-30700) - (25)(-30400)) = y/((-30400)(22) - (-30700)(25)) = 1/((25)(25) - (22)(22))`

⇒ `x/(7600 - 6754) = y/(7675 - 6688) = 100/(3 xx 47)`

⇒ `x/846 = y/987 = 100/(3 xx 47)`

⇒ `x = (100 xx 846)/(3 xx 47), y = (100 xx 987)/(3 xx 47)`

⇒ x = 600, y = 700

Hence, the cost of chair and table are Rs. 600 and Rs. 700 respectively.