Question

Rama purchased a gold ring at $ 20\% $ discount on the marked price but she sold it at the marked price. Find Rama’s gain percent on this transaction.

Answer 1

Hint: First of all suppose the marked price as to be and then convert the given word statements in the form of mathematical expression and then will calculate the cost price and once the cost price is found, then selling price will be calculated then the will find gain and then will find its percentage.

Complete step-by-step answer:
Let us assume that the Marked price be Rs. $ 100 $
Given that, Rama purchased a gold ring at $ 20\% $ discount on the marked price
Therefore, $ 20\% $ of Rs. $ 100 $ is
 $ = \dfrac{{20}}{{100}} \times 100 $
Common factors from the numerator and the denominator cancel each other.
 $ = 20 $ Rs.
So, the cost price $ = $ Marked price $ - $ discount
Place the values in the above equation –
Cost price $ = 100 - 20 $
Cost price $ = Rs.80 $
Given that the selling price is the same as the marked price.
Selling price $ = Rs.100 $
Profit is when the selling price is greater than the cost price and it can be calculated by its difference.
Profit $ = 100 - 80 $
Profit $ = Rs.20 $
Profit $ \% = \dfrac{{\Pr ofit}}{{\cos t{\text{ price}}}} \times 100 $
Place the values –
Profit $ \% = \dfrac{{20}}{{80}} \times 100 $
Simplify the above expression removing the common factors from the numerator and the denominator.
Profit $ = 25\% $
Hence, Rama gained $ 25\% $ on this transaction.
So, the correct answer is “ $ 25\% $ ”.

Note: Gain is also known as the profit. When the selling price is greater than the cost price then there is always profit. Remember that the discount is always calculated on the marked price. Always start this type of problems assuming respective variables such as x or any value such as tens and hundreds so that it would be easy to convert in percentage.