Jamila sold a table and a chair for ₹ 1050, thereby making a profit of 10% on a table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got ₹ 1065. Find the cost price of each.

Given:

Jamila sold a table and a chair for ₹ 1050, thereby making a profit of 10% on a table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got ₹ 1065.

To do:

We have to find the total cost price of each.

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

Selling price of the table when it is sold at a profit of 10%$=x+\frac{10}{100}x=1.1x$

Selling price of the chair when it is sold at a profit of 25%$=y+\frac{25}{100}y=1.25y$

Selling price of the table when it is sold at a profit of 25%$=x+\frac{25}{100}x=1.25x$

Selling price of the chair when it is sold at a profit of 10%$=y+\frac{10}{100}y=1.1y$

According to the question,

$1.1x + 1.25y = 1050$.....(i)

$1.25x + 1.1y = 1065$.....(ii)

Multiplying equation (i) by 1.1 on both sides, we get,

$1.1(1.1x+1.25y)=1.1(1050)$

$1.21x+1.375y=1155$.....(iii)

Multiplying equation (ii) by 1.25 on both sides, we get,

$1.25(1.25x+1.1y)=1.25(1065)$

$1.5625x+1.375y=1331.25$.....(iv)

Subtracting equation (iii) from equation (iv), we get,

$(1.5625x+1.375y)-(1.21x+1.375y)=1331.25-1155$

$1.5625x-1.21x+1.375y-1.375y=176.25$

$0.3525x=176.25$

$x=\frac{176.25}{0.3525}$

$x=\frac{1762500}{3525}$

$x=500$

Substituting $x=500$ in equation (ii), we get,

$1.25(500)+1.1y=1065$

$625+1.1y=1065$

$1.1y=1065-625$

$1.1y=440$

$y=\frac{440}{1.1}$

$y=\frac{4400}{11}$

$y=400$

The cost of the table is Rs. 500 and the cost of the chair is Rs. 400.   

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Updated on: 10-Oct-2022

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