Multiple choice

On selling an article for Rs. 96, a person finds that his loss % is one fourth of the amount of rupees that he paid for the article. What can be the cost price ? एक वस्तु को 96 रू. में बेचने पर एक व्यक्ति ज्ञात करता है कि उसका हानि प्रतिशत उसके द्वारा वस्तु को खरीदने पर अदा की गयी राशि का एक चौथाई है। क्रय मूल्य क्या हो सकता है ?

  1. Rs. 160 only / केवल 160 रू.

  2. Rs. 240 only / केवल 240 रू.

  3. Either Rs. 160 or Rs. 240 या तो 160 रू. या 240 रू.

  4. Neither Rs. 160 nor Rs. 240 न तो रू. 160 न ही 240 रू.
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C Correct answer
Explanation

Let CP = x. Loss = x - 96. Given loss percent = x/4, so (x-96)/x × 100 = x/4. This gives 400(x-96) = x², or x² - 400x + 38400 = 0. Using quadratic formula: x = [400 ± √(160000 - 153600)]/2 = [400 ± √6400]/2 = [400 ± 80]/2. This gives x = 240 or x = 160. Both values are valid cost prices, so the answer could be either Rs. 160 or Rs. 240.

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