Question

A man sold a chair and a table together for ₹1520 there by making a profit of 25% on
the chair and 10% on table. By selling them together for₹ 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 Cost Price of chair be ₹ x

and

• Let Cost Price of table be ₹ y

Case :- 1

We know,

$\sf \: Selling Price = \dfrac{(100 + Profit\%) \times Cost Price}{100}$

According to statement,

• A profit of 25% on the chair and 10% on table.

So,

$\sf \: Selling Price_{(chair)} = \dfrac{(100 + 25) \times x}{100}$

$\sf \: Selling Price_{(chair)} = \dfrac{(125) \times x}{100}$

$\bf\implies \: \: Selling Price_{(chair)} = \dfrac{5x}{4}$

and

$\sf \: Selling Price_{(table)} = \dfrac{(100 + 10) \times y}{100}$

$\sf \: Selling Price_{(table)} = \dfrac{(110) \times y}{100}$

$\bf\implies \: \: Selling Price_{(table)} = \dfrac{11y}{10}$

According to statement,

$\rm :\longmapsto\:Selling Price_{(chair)} + Selling Price_{(table)} = 1520$

$\rm :\longmapsto\:\dfrac{5x}{4} + \dfrac{11y}{10} = 1520$

$\rm :\longmapsto\:\dfrac{25x + 22y}{20} = 1520$

$\rm :\implies\:25x + 22y = 30400 - - - (1)$

Case :- 2

According to statement,

A profit of 10% on the chair and 25% on the table.

So,

$\sf \: Selling Price_{(chair)} = \dfrac{(100 + 10) \times x}{100}$

$\sf \: Selling Price_{(chair)} = \dfrac{(110) \times x}{100}$

$\bf\implies \:Selling Price_{(chair)} = \dfrac{11x}{10}$

Also,

$\sf \: Selling Price_{(table)} = \dfrac{(100 + 25) \times y}{100}$

$\sf \: Selling Price_{(table)} = \dfrac{(125) \times y}{100}$

$\bf\implies \:Selling Price_{(table)} = \dfrac{5y}{4}$

According to statement,.

$\rm :\longmapsto\:Selling Price_{(chair)} + Selling Price_{(table)} = 1535$

$\rm :\longmapsto\:\dfrac{11x}{10} + \dfrac{5y}{4} = 1535$

$\rm :\longmapsto\:\dfrac{22x + 25y}{20} = 1535$

$\rm :\implies\:22x + 25y = 30700 - - - (2)$

On adding equation (1) and (2), we get

$\rm :\longmapsto\:47x + 47y = 61100$

$\rm :\implies\:x + y = 1300 - - - (3)$

On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\: - 3x + 3y = 300$

$\rm :\implies\: - x + y = 100 - - - (4)$

On adding equation (3) and (4), we get

$\rm :\longmapsto\:2y = 1400$

$\bf\implies \:y \: = \: 700$

On substituting y = 700 in equation (3), we get

$\rm :\longmapsto\:x + 700 = 1300$

$\bf\implies \:x \: = \: 600$

Hence,

• Cost Price of chair = ₹ 600

and

• Cost Price of table = ₹ 700