Question

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 1

(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.