Question

If a person were to sell a sofa set for Rs.7200 he would loss \[20\% \] for what must be sold to gain \[20\% \].

Answer 1

Hint: In these kinds of problems, we need to think about cost price, selling price and the comparison of both prices. Cost price is the price of an object at which the person buys it. Selling price is the price of an object, when he is selling the same object to others.
If the cost price(cp) is greater than the selling price(sp), that means the person bought it at a high price and is selling for a low price, so he will get a loss. Similarly, he will get profit if the selling price is more than loss.
Loss/profit percentage is always calculated with respect to the cost price.
This is the logic behind the formulas we use.

Formula used:
(1) \[cp = \left( {\dfrac{{100}}{{100 - loss\% }}} \right) \times sp\]
(2) \[sp = \left( {\dfrac{{100 + gain\% }}{{100}}} \right) \times cp\]

Complete step-by-step answer:
It is given that the selling price of the sofa set is Rs.7200.It is also given that it would be a loss of 20% if the sofa set is sold at Rs.7200
The question is about finding the selling price to gain 20%.But before that we have to find the cost price of the sofa set using given details.
Now we are going to use the formula of cost price.
\[cp = \left( {\dfrac{{100}}{{100 - loss\% }}} \right) \times sp\]
Now we are going to substitute the value of the selling price of Rs.7200 and loss of 20% on the above formula to get the value of the cost price.
\[ \Rightarrow cp = \dfrac{{7200}}{{100 - 20}} \times 100\]
\[ \Rightarrow cp = \dfrac{{7200}}{{80}} \times 100\]
Now we are going to divide 7200 by 80 and then we multiply it by 100.
\[ \Rightarrow cp = 90 \times 100\]
\[ \Rightarrow cp = 9000\]
Finally we found that the cost price of the sofa set is Rs.9000
Now our aim is to find the value of the selling price of the sofa set to gain 20%
Now we are going to use the formula of selling price.
\[sp = \left( {\dfrac{{100 + gain\% }}{{100}}} \right) \times cp\]
Now we are going to substitute the value of the cost price of Rs.9000 and gain 20% on the above formula to find the selling price.
\[sp = \dfrac{{100 + 20}}{{100}} \times 9000\]
\[ \Rightarrow sp = \dfrac{{120}}{{100}} \times 9000\]
Now we are going to simplify the above expression to find the selling price. First we divide 9000 by 100 then multiply it by 120.
Then we get, \[sp = 10800\]
Finally we found that the selling price of the sofa set is Rs.10800

Hence we can conclude that it should be sold at Rs.10800 to get \[20\% \]gain.
Note:
The Cost price is the price at which a thing is purchased. The selling price is the price at which a thing is sold. Even if you don’t remember the formula, you can derive it on your own as follows.
Loss(L) = Cost price(C.P) - Selling price(S.P)
We calculate the loss percentage with respect to the cost price, so it will be
Loss % =${\dfrac{L}{C.P.}}$$\times 100$