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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.
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