Question

A shopkeeper buys paper at Rs. $ 50 $ per ream. At what price per quire should be sell it to gain $ 20\% ? $

Answer 1

Hint: Here take $ 1 $ ream is equal to $ 20 $ quires. First find the price of quire from the ream and then find the selling price to get the specified $ 20 $ percentage of the gain. Convert the percentage in the form of fraction and simplify the equation.

Complete step-by-step answer:
Given that buying price is Rs. $ 50 $ per ream
Also, $ 1 $ ream $ = 20 $ quires.
So, the shopkeeper gets $ 20 $ quires at Rs. $ 50 $
Therefore, $ 1 $ quire $ = ? $
Do cross-multiplication –
 $
   = \dfrac{{50 \times 1}}{{20}} \\
   = \dfrac{{50}}{{20}} \;
  $
Now, to gain $ 20 $ percent, the selling price per quire will be the sum of the cost price and $ 20 $ percent of the cost price.
 $ = \dfrac{{50}}{{20}} + \left( {\dfrac{{50}}{{20}} \times \dfrac{{20}}{{100}}} \right) $
Simplify the above equation – the common factors from the numerator and the denominator cancel each other
 $ = \dfrac{{50}}{{20}} + \left( {\dfrac{{50}}{1} \times \dfrac{1}{{100}}} \right) $
Take common factors from the first part of the equation and remove them.
 $ = \dfrac{5}{2} + \left( {\dfrac{{50}}{{100}}} \right) $
Take common factors from the second part of the equation and remove them.
 $ = \dfrac{5}{2} + \left( {\dfrac{1}{2}} \right) $
When we have common base or the denominator directly add the numerator part of the equation –
 $ = \dfrac{{5 + 1}}{2} $
Simplify the equation –
 $ = \dfrac{6}{2} $
Take common from the denominator and the numerator
 $ = Rs.{\text{ 3}} $
Hence, the required answer is – the shopkeeper must sell the quire at Rupees $ 3 $ to get the gain of $ 20 $ percent.
So, the correct answer is “3 Rs”.

Note: Always know the basic conversion relation to convert the required units of measurement since it is the sole dependency of the question. Be careful while simplifying the percentage into the fraction and simplify the solution as per the requirements. Know the basic concepts of LCM (least common multiple) to simplify the unlike fractions.