Question

A man sold a chair and a table for Rs.760 thereby making a profit of 25% on chair and 10% on table. By selling them together for Rs.767.50 he would have made a profit of 10% on chair and 25% on table. Find cost price of each?

Answer 1

You can solve this using linear equations. As follows:

let the price of the table be y and that of the chair be x:

equation 1:
price of chair at 25% profit will be 1.25x (that is 125% of marked price x) and profit is 0.25x
price of table at 10% profit is 1.1y (that is 110% of y)
 
Therefore   1.1y + 1.25x= Rs.760

equation 2:

price of chair at 10% profit = 1.1x
price of table at 25% profit= 1.25y

Therefore 1.1x + 1.25y = 767.5

Solve for x and y:

1.25x+1.1y= 760..........1.1y= 760-1.25x.......y= (760-1.25x)/1.1
1.1x+1.25y= 767.5.......

substitute y in the second equation

            1.1x + 1.25((760-1.25x)/1.1)=767.5
            1.21x+950-1.5625x= 844.25
            -0.3525x= -105.75
                        x=  300

next, substitute x in any of the above equations to find y:
1.1y=760- 1.25x
1.1y= 760- 375
1.1y= 385
  y=  350

therefore the cost price of the chair=  Rs. 300
   and that of the table = Rs.350

Answer 2

Answer:

and profit is 0.25x

price of table at 10% profit is 1.1y (that is 110% of y)

 

Therefore   1.1y + 1.25x= Rs.760

equation 2:

price of chair at 10% profit = 1.1x

price of table at 25% profit= 1.25y

Therefore 1.1x + 1.25y = 767.5

Solve for x and y:

1.25x+1.1y= 760..........1.1y= 760-1.25x.......y= (760-1.25x)/1.1

1.1x+1.25y= 767.5.......

substitute y in the second equation

            1.1x + 1.25((760-1.25x)/1.1)=767.5

            1.21x+950-1.5625x= 844.25

            -0.3525x= -105.75

                        x=  300

next, substitute x in any of the above equations to find y:

1.1y=760- 1.25x

1.1y= 760- 375

1.1y= 385

  y=  350

therefore the cost price of the chair=  Rs. 300

   and that of the table = Rs.350