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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 beÂ xÂ and cost of table beÂ y.

â‡’Â  As per the question,
â‡’Â Â x+25xâ€‹/100+y+10yâ€‹/100=1520

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

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