A chair and a table cost Rs 1800. If by selling the table at 15% profit, and the chair at 10% loss, a total profit of 6% is made. What is the cost price of a chair?

A profit or loss is the difference between the cost price and the selling price. If the cost price is more than the selling price, then the transaction results in a loss, whereas if the selling price is more than the cost price then the transaction results in a profit.

Answer: For a chair and a table costing Rs 1800 where the table is sold at 15% profit and the chair is sold at 10% loss having a total profit of 6% overall, the cost price of the chair is Rs 648.

A profit% or loss% is calculated always on the cost price, that is Profit% or Loss% = (Profit or Loss)/CP × 100

Explanation:

Let the cost price of the chair be 'x' and then the cost price of the table be '(1800 - x)'.

Let the selling price of the table be SP₁, since the table is sold at 15% profit, therefore:

Profit% = (SP - CP)/CP × 100

or, 15 = ((SP₁ - (1800 - x))/(1800 - x)) × 100

or, 15/100 = (SP₁ - 1800 + x)/(1800 - x)

or, 15 × (1800 - x) =  100 × (SP₁ - 1800 + x)

or, 15 × (1800 - x) =  100SP₁ - 180000 + 100x

or, 27000 - 15x = 100SP₁ - 180000 + 100x

or, 100SP₁ = 27000 - 15x +180000 - 100x

or, 100SP₁ = 207000 - 115x

or, SP₁ = (207000 - 115x)/100

Let the selling price of the table be SP₂, since the chair is sold at 10% loss, therefore:

Loss% = (CP - SP)/CP × 100

or, 10 = (x - SP₂ )/x × 100

or, 10/100 = (x - SP₂ )/x

or, 10x = 100 × (x - SP₂ )

or, 10x = 100x - 100SP₂

or, 100SP₂ =  100x - 10x

or, 100SP₂ = 90x

or, SP₂ = 90x/100

Now let's consider the total profit condition for both the table and chair combined:

Total selling price = SP₁ + SP₂ = (207000 - 115x)/100 + 90x/100

= (207000 - 115x + 90x)/100

= (207000 - 25x)/100

Total cost price = Rs 1800

Total profit = 6%

Using the profit% formula and substituting the values, we get:

Profit% = (SP - CP)/CP × 100

or, 6 = (((207000 - 25x)/100 - 1800)/1800) × 100

or, 6/100 = (207000 - 25x -180000)/1800

or, 6 = (27000 - 25x)/1800

or, 6 × 1800 = 27000 - 25x

or, 10800 = 27000 - 25x

or, 25x = 27000 - 10800

or, 25x = 16200

or, x = 16200/25 = 648

Therefore the cost price of the chair is = x = Rs 648.