Question

a men sells an article at a gain of 50%.If he had sold it at rupees 63 less ,he would have lost 20%.Find the cost of the article.​

Answer 1

Let the cost price of the article be x.

As per the Question, the man sold the article at a gain of 50%

Hence,

Selling price = x + 50% of x

$\rm\dashrightarrow x + \dfrac{50}{100} \ of \ x$

$\rm\dashrightarrow x + \dfrac{50}{100} \times x$

$\rm\dashrightarrow x + \dfrac{50x}{100}$

$\rm\dashrightarrow x + \dfrac{x}{2}$

$\rm\dashrightarrow \dfrac{3x}{2}$

Now according to the condition,

If he had sold it at rupees 63 less ,he would have lost 20%.

Hence,

Selling price - 63 = cost price - 20% of cost price.

$\dashrightarrow\rm \dfrac{3x}{2} - 63 = x - \dfrac{20x}{100}$

$\dashrightarrow\rm \dfrac{3x}{2} - 63 = x - \dfrac{x}{5}$

$\dashrightarrow\rm \dfrac{3x}{2} - 63 = \dfrac{5x - x}{5}$

$\dashrightarrow\rm \dfrac{3x}{2} - 63 = \dfrac{4x}{5}$

$\dashrightarrow\rm - 63 = \dfrac{4x}{5}-\dfrac{3x}{2}$

$\dashrightarrow\rm - 63 = \dfrac{8x}{10} - \dfrac{15x}{10}$

$\dashrightarrow\rm - 63 = \dfrac{8x-15x}{10}$

$\dashrightarrow\rm - 63 = \dfrac{-7x}{10}$

$\dashrightarrow\rm 63 = \dfrac{7x}{10}$

$\dashrightarrow\rm x = \dfrac{63\times 10}{7}$

$\dashrightarrow\bf x = 90$

Cost price = x = 90

Hence, cost price of the article is ₹90.