Question

Jamila sold a table and a chair for Rs.1050, thereby making a profit of 10% on a table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair, she would have got Rs.1065. Find the cost price of each.

Answer 1

Hint: In this question, we need to determine the cost price of the table and the chair for Jamila. For this, we will establish two simultaneous equations for the selling prices of the commodities and solve them to get the result.

Complete step-by-step answer:
Let the cost price of the table and the chair for Jamila be ‘x’ and ‘y; respectively.
According to the question, Jamila makes a profit of 10% on the table and 25% on the chair such that the selling price of the table and the chair is Rs.1050.
So, the selling price of the table will be given as
 $
  S{P_t} = C{P_t} + {\text{Profit}} \\
   = x + \dfrac{{10}}{{100}}x \\
   = 1.1x \\
  $
Similarly, the selling price of the chair will be given as
 $
  S{P_c} = C{P_c} + {\text{Profit}} \\
   = y + \dfrac{{25}}{{100}}y \\
   = 1.25y \\
  $
Hence, the total selling price will be given as:
 $
  SP = S{P_t} + S{P_c} \\
  1050 = 1.1x + 1.25y - - - - (i) \\
  $
Again, if the profit percent on the table and the chair for the Jamila has been reversed such that the new profit percent are 25% on a table and 10% on a chair.
So, the new selling price of the table will be given as:
 $
  SP{'_t} = C{P_t} + {\text{Profit}} \\
   = x + \dfrac{{25}}{{100}}x \\
   = 1.25x \\
  $
Similarly, the new selling price of the chair will be given as:
 $
  SP{'_c} = C{P_c} + {\text{Profit}} \\
   = y + \dfrac{{10}}{{100}}y \\
   = 1.1y \\
  $
It is being given that the new selling price of the table and the chair is Rs.1065.
So,
 $
  SP' = SP{'_t} + SP{'_c} \\
  1065 = 1.25x + 1.1y - - - - (ii) \\
  $
Solving the equations (i) and (ii) by multiplying equation (i) by 1.25 and equation (ii) by 1.1 and then subtract them to determine the cost price of the table and the chair.
 $
  \left( {1.1x + 1.25y} \right)1.25 = 1050 \times 1.25 \\
   \Rightarrow 1.375x + 1.5625y = 1312.5 - - - - (a) \\
    \\
  \left( {1.25x + 1.1y} \right)1.1 = 1065 \times 1.1 \\
   \Rightarrow 1.375x + 1.21y = 1171.5 - - - - (b) \\
  $
Now, subtracting the equations (a) and (b)
 $
  \left( {1.375x + 1.5625y} \right) - \left( {1.375x + 1.21y} \right) = 1312.5 - 1171.5 \\
  y(1.5625 - 1.21) = 141 \\
  y = \dfrac{{141}}{{0.3525}} \\
   = 400 \\
  $
Hence the value of the cost price of the chair is Rs.400.
Substitute the value of the cost price of the chair in the equation (i), we get
 $
  1.1x + 1.25y = 1050 \\
  1.1x + 1.25(400) = 1050 \\
  1.1x + 500 = 1050 \\
  1.1x = 1050 - 500 \\
  x = \dfrac{{550}}{{1.1}} \\
   = 500 \\
  $
Hence, the value of the cost price of the table is Rs.500.

Note: It is worth noting here that in the question, the total selling price of the table and the chair have been given instead of the individual selling price and so, the equation generated will result in the total selling price only.