Answer

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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.

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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