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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.
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Solution
S.P. of an article = Rs. 21
Let cost price = Rs. x
Then loss = x%
∴ S.P. = `("C.P." (100 - "loss"%))/(100)`
21 = `(x(100 - x))/(100)`
2100 = 100x - x2
⇒ x2 – 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.
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