Question

By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.

Answer 1

S.P. of an article = Rs. 21
Let cost price = Rs. x
Then loss = x%

∴ S.P. = ${\displaystyle \frac{\text{C.P.}(100-\text{loss}\%)}{100}}$

21 = ${\displaystyle \frac{x(100-x)}{100}}$

2100 = 100x - x²
⇒ x^{2 –} 100x + 2100 = 0
⇒ x² – 30x – 70x + 2100 = 0
⇒ x(x – 30) – 70(x – 30) = 0
⇒ (x – 30)(x – 70) = 0
EIther x – 30 = 0,
then x = 30
or
x - 70 = 0,
then x = 70
∴ Cost price = Rs. 30 or Rs. 70.