Question

On selling a chair at $ Rs.720 $ , a man gains $ 20\% $ . Find the C.P of the chair.

Answer 1

Hint: As we know that the above question is related to the topic of percentage. Percentage means a number or a ratio represented in the form of fractions of $ 100 $ . We know that the price at which any product is sold is called the selling price of the product. It is denoted by S.P. And the price at which a product is brought is the cost price of the product and it is denoted by C.P.

Complete step by step solution:
Here in the question we have been given the selling price of the product which is $ 720 $ . Gain% is also given i.e. $ 20\% $ . We have to find the cost price of the chair.
According to the question we can say that the selling price is the total cost price of the chair along with gain on the price. It means $ S.P = C.P + 20\% \times C.P $ .
Let the cost price be $ x $ . Therefore putting this in the equation we have: $ x + 20\% \times x = 720 $ . We will now solve it.
 $ \Rightarrow x + \dfrac{{20}}{{100}}x = 720 \\
\Rightarrow \dfrac{{100x + 20x}}{{100}} = 720
 $ .
On further solving we have,
 $ \dfrac{{120x}}{{100}} = 720 \\
\Rightarrow 120x = 720 \times 100
 $ .
We will now isolate the term $ x $ , it gives: $ x = \dfrac{{72000}}{{120}} = 600 $ .
Hence the cost price i.e. C.P of the chair is $ Rs.600 $ .
So, the correct answer is “ $ Rs.600 $ ”.

Note: Before solving this kind of question we should be aware of the cost price, selling price, grain or loss of their formulas and their properties. We can solve this kind of question in many ways, here we have solved it by directly applying the formula of Cost price. We can make errors if we do not know the formula or the correct procedure to get the answer.