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# A man sold a chair and a table together for Rs. 1520 thereby making a profit of 25% on the 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

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An important question from linear equations in two variables as it was already asked in various examinations in which we have to find the value of a chair and a table if the total selling price of a chair and a table is 1520 and the profit % in a 10% on chair and 15% on table and if the profit% is 10% on chair and 25% on table then the total selling price is 1535.

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 30

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1. ## Let the cost of chair be x and cost of table be y.

As per the question,
x+25x​/100+y+10y​/100=1520

125x+110y=152000
25x+22y=30400                —— ( 1 )
And also from the question, we get
x+10x​/100+y+25y/100=1535
110x+125y=153500
22y+25y=30700           —— ( 2 )
Now, Multiply equation ( 1 ) with 22 and equation ( 2 ) with 25 we get,
550x+484y=668800          —–  ( 3 )
550x+625y=767500           —— ( 4 )
Now, subtracting equation ( 2 ) by ( 1 ) we get,
y=700
Substituting value of y in equation ( 1 ) we get,
x=600
Cost price of chair is Rs.600 and cost price of table is Rs.700.

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