Question

The cost price of 4 chairs and 5 tables is Rs. 330 .if the chairs are sold at 25% loss nd tables at 25% profit the total selling price is rs. 372.50 the cost price of chair is??

Answer 1

Answer:  The required cost of one chair is Rs. 20.

Step-by-step explanation:  Given that the cost price of 4 chairs and 5 tables is Rs. 330 . If the chairs are sold at 25% loss and tables at 25% profit the total selling price is rs. 372.50.

We are to find the cost of one chair.

Let Rs x and Rs y represents the cost price of 1 chair and 1 table respectively.

Then, according to the given information, we have

$4x+5y=330~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$4\left(x-25\%\times x\right)+5\left(y+25\%\times y\right)=372.50\\\\\\\Rightarrow 4\left(x-\dfrac{x}{4}\right)+5\left(y+\dfrac{y}{4}\right)=372.50\\\\\\\Rightarrow 3x+\dfrac{25y}{4}=372.50\\\\\\\Rightarrow 12x+25y=1490~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by 3 and then subtracting from equation (ii), we get

$(12x+25y)-(12x+15y)=1490-3\times330\\\\\Rightarrow 10y=1490-990\\\\\Rightarrow 10y=500\\\\\Rightarrow y=\dfrac{500}{10}\\\\\Rightarrow y=50.$

Substituting the value of y in equation (i), we get

$4x+5\times50=330\\\\\Rightarrow 4x+250=330\\\\\Rightarrow 4x=330-250\\\\\Rightarrow 4x=80\\\\\Rightarrow x=\dfrac{80}{4}\\\\\Rightarrow x=20.$

Thus, the required cost of one chair is Rs. 20.