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A man sold a chair and a table together ...

A man sold a chair and a table together for 760 thereby making a profit of 25% on the chair and 10% on the table. By selling them together for 767.50 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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Let the cost price of chair = Rs. X and the cost price of table = Rs. Y
Now, two cases arise :
Case I : 25% profit on chair and 10% profit on table
Selling price of table = Rs. `(x + (25x)/(100)) = Rs. (125x)/(100)`
Selling price of table = Rs. `(y + (10y)/(100)) = Rs. (110y)/(100)`
But total S.P. = Rs. 760
`therefore (125x)/(100) + (110y)/(100) = 760 implies 125x + 100y = 76000`
`implies 25x + 22y = 15200 " ...(1)"`
Case II : 10% profit on chair and 25% profit on table
Selling price of chair = Rs. `(x + (10x)/(100)) = Rs. (110x)/(100)`
Selling price of table = Rs. `(y + (25y)/(100)) = Rs. (125y)/(100)`
But total S.P. = Rs. 767.50
`therefore (110x)/(100) + (125y)/(100) = 767.50 implies 110x + 125 y = 76750`
implies 22x + 25y = 15350 ...(2)
To solve equations (1) and (2), adding equations (1) and (2), we get
47x + 47y = 30550
implies x + y = 650 ...(3)
Subtracting equation (2) from (1), we get
3x - 3y = - 150
implies x - y = - 50 ...(4)
On adding equations (3) and (4), we get
2x = 600 implies x = 300
Putting x = 300 in equations (3), we get
300 + y = 650 implies y = 650 - 300 = 350
`therefore` Cost of chair = Rs. 300 and cost of table = Rs. 350
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