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 × x + (100+10)/100 × 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 × x +( 100 +25)/100 × 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 × 47)`
`⇒x/846 = y/987 = 100/(3 × 47)`
`⇒ x = (100 × 846)/(3 × 47), y = (100 × 987)/(3 × 47)`

⇒ x = 600, y = 700
Hence, the cost of chair and table are Rs.600 and Rs.700 respectively.