Question

A shopkeeper who deals in books sold a book at $16\% $ loss. Had she charged an additional $Rs.60$ while selling it, her profit would have been $14\% $. Find the cost price, in rupees, of the book?

Answer 1

Hint: Assume the cost price be x. by using formula $gain\% = \dfrac{{S.P - C.P}}{{C.P}} \times 100$ and $loss\% = \dfrac{{C.P - S.P}}{{S.P}} \times 100$. solve for x to get the cost price.

Complete Step by Step Solution:
Let the cost price be x.
Then the selling price be $x - \dfrac{{16x}}{{100}}$
By taking lcm as hundred and solving we get
$
   \Rightarrow \dfrac{{100x - 16x}}{{100}} \\
   \Rightarrow \dfrac{{84x}}{{100}} = \dfrac{{21x}}{{25}} \\
 $
Now , if the selling price is sixty more , then the profit is 14%.
Now we can write it as
$ \Rightarrow \dfrac{{21x}}{{25}} + 60 = x + \dfrac{{14x}}{{100}}$
By taking LCM as hundred on right hand side and solving we get
$
   \Rightarrow \dfrac{{21x}}{{25}} + 60 = \dfrac{{100x + 14x}}{{100}} \\
   \Rightarrow \dfrac{{21x}}{{25}} + 60 = \dfrac{{114x}}{{100}} \\
 $
By taking x terms to one side and constant terms to one side we get
$ \Rightarrow \dfrac{{114x}}{{100}} - \dfrac{{21x}}{{25}} = 60$
Now the LCM of 100 and 25 is 50 we get
$
   \Rightarrow \dfrac{{57x - 42x}}{{50}} = 60 \\
   \Rightarrow \dfrac{{\left( {57 - 42} \right)x}}{{50}} = 60 \\
   \Rightarrow \dfrac{{15x}}{{50}} = 60 \\
 $
On cancellation in five table we get
$ \Rightarrow \dfrac{{3x}}{{10}} = 60$
On multiplying with ten on both sides we get
$
   \Rightarrow \dfrac{{3x}}{{10}} \times 10 = 60 \times 10 \\
   \Rightarrow 3x = 600 \\
 $
By dividing with three on both sides we get
$
   \Rightarrow \dfrac{{3x}}{3} = \dfrac{{600}}{3} \\
   \Rightarrow x = 200 \\
 $

Therefore, the cost price is Rs.200.

Note :
We could have also solved the question by finding the selling price in case of gain and selling price in case of loss in terms of x and then use the relation $S{P_{gain}} = S{P_{loss}} + 16.5$.