Question

Manila 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

Solution :-

Let the Cost Price of the table and chair be Rs. x and Rs. y respectively.

Situation - 1 (Selling Price of a table and a chair is Rs. 1050 with 10 % profit earned on table and 25 % profit earned on chair.)

Table - 10 % profit earned.

So, Selling Price of the table is -

⇒ SP = x + (x*10)/100

⇒ x + x/10 = 11x/10

So, SP of table is Rs. 11x/10

Chair - 25 % profit earned.

So, Selling Price of the chair is -

⇒ SP = y + (y*25)/100

⇒ y + y/4 = 5y/4

So, SP of chair is Rs. 5y/4

Now, according to the question.

⇒ 11x/10 + 5y/4 = 1050

Taking LCM of denominators and then solving it.

⇒ (22x + 25y)/20 = 1050

⇒ 22x + 25y = 1050*20

⇒ 22x + 25y = 21000 ....................(1) 

Situation - 2 (If Manila had taken a profit of 25 % on the table and 10 % on the chair, she would have got Rs. 1065)

Table - 25 % profit earned.

So, Selling Price of the table is -

⇒ SP = x + (x*25)/100

⇒ x + x/4 = 5x/4

So, selling price of the table is Rs. 5x/4

Chair - 10 % profit earned.

So, Selling Price of the chair is - 

⇒ SP = y + (y*10)/100

⇒ y + y/10 = 11y/10

Now, according to the question.

⇒ 5x/4 + 11y/10 = 1065

Taking the LCM of denominators and then solving it.

⇒ (25x + 22y)/20 = 1065

⇒ 25x + 22y = 1065*20

⇒ 25x + 22y = 21300 .......................(2)

Now, multiplying equation (1) by 25 and equation (2) by 22, we get

⇒ 550x + 625y = 525000 ............(3)

⇒ 550x + 484y = 468600 ............(4)

Now, subtracting (3) from (4).

   550x + 625y = 525000

   550x + 484y = 468600
 -          -           -  
_____________________

             141y = 56400
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⇒ 141y = 56400

⇒ y = 56400/141

⇒ y = 400

Substituting y = 400 (1)

22x + 25y = 21000

⇒ 22x + (25*400) = 21000

⇒ 22x + 10000 = 21000

⇒ 22x = 21000 - 10000

⇒ 22x = 11000

⇒ x = 11000/22

⇒ x = 500

So, Cost price of table is Rs. 500 and Cost Price of chair is Rs. 400 respectively.

Answer.