Question

A man purchase a chair and a table in total rupees 25800. he sold table at 13% profit and chair at 17% profit. if he sold table at 17% profit and chair at 13% profit then he get 80 rupees more profit. find cost price of both separately

Answer 1

The cost of chair is 11900 Rs. and cost of table is 13900 Rs.

Step-by-step explanation:

Let the cost of the chair be x and table be y

According to the question

$x+y=258000$  .................... (1)

On selling the table at 13% profit and chair at 17% profit, sell price

$S=(x+0.17x)+(y+0.13y)$

$\implies S=1.17x+1.13y$

Similarly, on selling the table at 17% profit and chair at 13% profit, the sell price

$S'=1.13x+1.17y$

According to the question

$S'-S=80$

$\implies 1.13x+1.17y -(1.17x+1.13y)=80$

$\implies -0.04x+0.04y=80$

$\implies -x+y=2000$      ................... (2)

Adding eq (1) and (2)

$2y=27800$

$\implies y=13900$ Rs.

Therefore,

$x=25800-13900$

$\implies x=11900$ Rs.

Therefore, the cost of chair is 11900 Rs. and cost of table is 13900 Rs.

Hope this answer is helpful.

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Answer 2

Cost price of table = Rs. 13,900

Cost price of chair = Rs. 11,900.

Step-by-step explanation:

Let cost price of table be x and cost price of chair be y respectively.

Given that:

x + y = 25800 --------------(1)

If table is sold at 13% profit and chair at 17% profit, we get:

SP = (x + 0.13x) + (y + 0.17y)

SP = 1.13x + 1.17y

If table is sold at 17% profit and chair at 13% profit, we get:

SP' = 1.17x + 1.13y

We know that SP' - S = 80

So 1.17x + 1.13y - (1.13x + 1.17y) = 80

     0.04x - 0.04y = 80

     4x - 4y = 8000

    x - y = 2000 ----------------(2)

Adding (1) and (2), we get:

  2x = 27800

Therefore x = 13900

Substituting in (1), we get:

 13900 + y = 25800

Therefore y =  11900

So, cost price of table = Rs. 13,900 and cost price of chair = Rs. 11,900.