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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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Hint: Try to find the selling price of one chair as well as one table.

Let the total price of one chair be Rs. x and that of one table to be Rs. Y.
Now it is given to us that Profit on a chair = 25%
$\therefore $ Selling Price of one chair= x+$\frac{{25x}}{{100}} = \frac{{125x}}{{100}}$
Now again we have given that Profit on a table =10%
$\therefore $Selling price of one table=y+$\frac{{10y}}{{100}} = \frac{{110y}}{{100}}$
Now according to the given condition we have given that the sum of the selling price of one chair and one table is 1520.
$\therefore $$\frac{{125x}}{{100}}$+$\frac{{110y}}{{100}}$=1520
Now since the denominator is same so we can add our numerators and on doing the cross multiplication, we have
$ \Rightarrow $ 125x+110y=152000
And hence on further simplification, we have
25x+22y=30400…………………(i)
Now according to the question if the profit on a chair is 10% and on a table is 25%
Then the total selling price is Rs.1535.
$\therefore $$\left( {x + \frac{{10x}}{{100}}} \right) + \left( {y + \frac{{25y}}{{100}}} \right) = 1535$
And hence again on taking the LCM and than on doing the cross multiplication, we have
110x+125y=153500
And hence on further simplification we have
22x+25y=30700.........................(ii)
Now on subtracting the equation (ii) from (i), we have
3x-3y=-300
And hence on taking 3 common and doing the simplification, we have
$ \Rightarrow $x - y=-100……………………..(iii)
Similarly on adding equation (i) and (ii), we have
47x+47y=61100
And hence on taking 47 common from both sides and on doing the simplification, we have
$ \Rightarrow $x + y =1300…………………(iv)
Now on adding equations (iii) and (iv) we have
2x=1200
And hence x=600
Now on putting the value of x in equation (iii) we get
$ \Rightarrow $600-y=-100
$ \Rightarrow $y=100+600=700
Hence the cost price of a chair is Rs. 600 and cost price of a table is Rs. 700.

Note: In this type of question first of all we have to find the selling price of the given materials and than according to the given condition we can find the cost price of the materials.

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