Question

Q.2 - A chair and a table together cost Rs 1800. If by selling the table
at a profit of 15% and the chair at a loss of 10% a total profit of 6% is
made, then what is the cost price of the chair?

PLEASE GIVE STEP BY STEP EXPLANATION

NO SPAMMING!!!​

Answer 1

Given:

Cost of a chair and table together = Rs. 1800

Total profit = 6%

Table sold at a profit of 15%.

Chair sold at a loss of 10%.

To find:

Cost price of chair = ?

Solution:

Let the cost price of a table = $x$ Rs.

So, cost of chair = (1800 - $x$) Rs.

Now, as per question:

$15\%\ of\ x-10\%\ of\ (1800-x) = 6\%\ of\ 1800$

($\because$ Loss is subtracted from profit and there is a total profit so equated to a positive term)

Now, solving the above equation:

$\dfrac{15}{100}\times x-\dfrac{10}{100}\times (1800-x) = \dfrac{6}{100}\times 1800\\\Rightarrow 15x -18000+10x = 10800\\\Rightarrow 25x=28800\\\Rightarrow x = 1152\ Rs.$

Now, cost of chair = (1800 - $x$) Rs = 1800 - 1152 = Rs. 648

So, the answer is:

Cost of chair = Rs. 648

Answer 2

Given :

The cost of the chair and the table together = Rs 1800

6% profit is made by selling the table at a profit of 15% and the chair at a loss of 10% .

To find :

Cost price of the chair .

Solution :

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

then , according to the question ,

x + y = 1800     ......(i)

6% profit is made by selling the table at a profit of 15% and the chair at a loss of 10% .

then ,

[ x + x * ( 15 / 100 ) ] + [ y - y * ( 10 / 100 ) ] = 1800 + 1800 * ( 6 / 100 )

=> ( 23 * x / 20 ) + ( 9 * y / 10 ) = 1908

=> 23 x + 18 y = 38160      ......(ii)

on solving the equations (i) and (ii) , we get ,x = 1152 and , y = 648

The cost price of the chair is Rs 648 .