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 Rs. 10 less then he 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

Hint- First we assume the cost price of the sunglasses will be Rs.x. After this we will calculate the selling price such that the gain is 25%. Again, according to given data, we will calculate the new cost price and new selling price. Finally we will calculate the gain %.

Complete step-by-step answer:
Let the original cost price of sunglasses be Rs,x.
For the gain to be 25%, the selling price is calculated by:
SP = CP + profit
Putting the values in above equation, we get:
SP= Rs.x +Rs.25% of x = = Rs.x +Rs.$\dfrac{{25}}{{100}}$ $ \times $ x = Rs.$\dfrac{{5x}}{4}$ .
Now, it is given that in the second case he is buying at 25% less price.
Therefore, the new cost price is given by:
New CP = original CP – 25% of original CP.
             = Rs. x - Rs.$\dfrac{{25}}{{100}}$ $ \times $ x = Rs. $\dfrac{{3x}}{4}$
It is also given that the new SP is Rs10 less than original SP.
Therefore, New SP = Rs.($\dfrac{{5x}}{4}$ -10).
New gain = New SP – New CP = Rs.($\dfrac{{5x}}{4}$ -10) - Rs. $\dfrac{{3x}}{4}$ =Rs.($\dfrac{x}{2}$-10).
We know that gain percent is given by:
Gain% = $\dfrac{{{\text{Gain}}}}{{{\text{CP}}}} \times 100\% $ =$\dfrac{{\dfrac{x}{2} - 10}}{{\dfrac{{3x}}{4}}} \times 100\% = \dfrac{{(2x - 40)}}{{3x}} \times 100\% $
According to question, we can write:
$\dfrac{{(2x - 40)}}{{3x}} \times 100$ = 40
$ \Rightarrow \dfrac{{(2x - 40)}}{{3x}} = \dfrac{{40}}{{100}} = \dfrac{2}{5}$
\[ \Rightarrow 5(2x - 40) = 6x\]
$ \Rightarrow $ 10x- 200 =6x
$ \Rightarrow $10x-6x = 200
$ \Rightarrow x = \dfrac{{200}}{4} = 50$
Therefore, the cost price of pair of sunglasses = Rs.50
So, option B is correct.

Note- In this type of question, you can use the formula for calculating the gain and loss if the cost price and selling price are given i.e. SP = CP+gain and SP=CP-Loss . We can also calculate the SP in case of gain % which is given by ${\text{CP = }}\dfrac{{{\text{SP}} \times {\text{100}}}}{{(100 + {\text{Gain percent)}}}}$ .