Question

veenita sold a table and a chair for Rs.1050,thereby making a profit of 10% on the 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

Define x and y:

Let the cost of the table be x

And the cost of the chair be y

Find the original selling price of the table and chair:

Profit from the table = 10% x = 0.1x

Selling Price of the table = x + 0.1x = 1.1x

Profit from the chair = 25% y = 0.25y

Selling Price of the chair = y + 0.25y = 1.25y

Total selling price = 1.1x + 1.25y

Form the equation:

The selling price is Rs 1050

1.1x + 1.25y = 1050

Find the new selling price of the table and chair:

Profit from the table = 25% x = 0.25x

Selling Price of the table = x + 0.25x = 1.25x

Profit from the chair = 10% y = 0.1y

Selling Price of the chair = y + 0.1y = 1.1y

Total selling price = 1.25x + 1.1y

Form the equation:

1.25x + 1.1y = 1065

Putting the 2 equations together:

1.1x + 1.25y = 1050 ----------------- [ 1 ]

1.25x + 1.1y = 1065----------------- [ 2 ]

[ 1 ] x 1.25 :      1.375x + 1.5625y = 1312.6 ---------------- [ 3 ]

[ 2 ] x 1.1  :       1.375x + 1.21y = 1171.50      ---------------- [ 4 ]

[ 3 ] - [ 4 ] :

0.3525y = 141

y = Rs 400  ----------------  sub into [ 1 ]

Find x:

1.1x + 1.25y = 1050

1.1x + 1.25 (400) = 1050

1.1x + 500 = 1050

1.1x = 550

x = Rs 500

Find the cost price:

Cost Price of the table = x = Rs 500

Cost Price of the chair = y = Rs 400

Answer: The cost price of the table is Rs 500 and the cost price of the chair is Rs 400