A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had

1.	A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Re 10 less, then be would have gained 40%. The cost price of the pair of sunglasses is (a) Rs 25 (b) Rs 50 (c) Rs 60 (d) Rs 70
Answer» (b) Rs 50 Let the C.P. of the pair of sunglasses be Rs x Then S.P. = \(\frac{X\times 125}{100}\) = Rs \(\frac{5X}{4}\) New C.P. = Rs \(\big(\frac{75}{100}\times X\big)\) = Rs \(\frac{3X}{4}\) New S.P. = Rs \(\big(\frac{5X}{4}-10\big)\) Given, \(\frac{5X}{4}\) - 10 = \(\frac{140}{100}\) x \(\frac{3X}{4}\) \(\Rightarrow\) \(\frac{5X}{4}\) - \(\frac{21X}{20}\) = 10 \(\Rightarrow\) \(\frac{25X-21X}{20}\) = 10 \(\Rightarrow\) 4x = 200 \(\Rightarrow\) x = Rs 50.

A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Re 10 less, then be would have gained 40%. The cost price of the pair of sunglasses is (a) Rs 25 (b) Rs 50 (c) Rs 60 (d) Rs 70

Answer»

(b) Rs 50

Let the C.P. of the pair of sunglasses be Rs x

Then S.P. = \(\frac{X\times 125}{100}\) = Rs \(\frac{5X}{4}\)

New C.P. = Rs \(\big(\frac{75}{100}\times X\big)\) = Rs \(\frac{3X}{4}\)

New S.P. = Rs \(\big(\frac{5X}{4}-10\big)\)

Given, \(\frac{5X}{4}\) - 10 = \(\frac{140}{100}\) x \(\frac{3X}{4}\) \(\Rightarrow\) \(\frac{5X}{4}\) - \(\frac{21X}{20}\) = 10

\(\Rightarrow\) \(\frac{25X-21X}{20}\) = 10

\(\Rightarrow\) 4x = 200

\(\Rightarrow\) x = Rs 50.