Question

a chair and a table cost Rs. 1200 . by selling the chair at a profit of 20%and the table at a lose of 5%, there is a profit of 4%on the whole. find the cost price of the table and the chair.​

Answer 1

The cost chair and table are Rs 432 and Rs 768 respectively.

Solution:

Given, a chair and a table cost Rs.1200  

Let, cost of chair be x and cost of table be y.

Then, x + y = 1200 → (1)

By selling the chair at a profit of 20% and the table at a loss of 5%, there is a profit of 4% on the whole.

Then, (x + 20% of x) + (y – 5% of y) = 1200 + 4% of 1200

$x+\frac{20}{100} \times x+y-\frac{5}{100} \times y=1200+\frac{4}{100} \times 1200$

$x\left(1+\frac{1}{5}\right)+y\left(1-\frac{1}{20}\right)=1200+4 \times 12$

$x\left(\frac{6}{5}\right)+y\left(\frac{19}{20}\right)=1248$ -- eqn 2

By multiplying the equation with 20, we get

24x + 19y = 1248 x 20

24x + 19y = 24960 → (3)

Now, solve (1) and (3)

-5x + 0 = -2160

x = 432

Now, substitute x value in (1)

y = 1200 – 432  = 768

Hence, the cost of chair and table are Rs 432 and Rs 768 respectively.