Question

By selling an A.C. for Rs.18000, I lose 20% .At what price should I sell it so that I get a profit of 10%?

Answer 1

Hint: We are given both percentage loss and percentage profit also on the same article. But the selling price is not the same for the second transaction because we have earned profit for the second time and suffered loss for the first time. So we will calculate the cost price that will help in finding the selling price of A.C.

Complete step-by-step answer:
Given that,
Transaction 1:
I sold the A.C. for Rs.18000 this is the S.P. of the A.C. but at a loss of 20%.
So, S.P. =18000 and %loss=20%
We will calculate the C.P. first.
Formula for percentage loss is given by,
\[\% loss = \dfrac{{loss}}{{C.P.}} \times 100\]
\[\% loss = \dfrac{{C.P. - S.P.}}{{C.P.}} \times 100\]
\[
   \Rightarrow \% loss = \dfrac{{C.P. - S.P.}}{{C.P.}} \times 100 \\
   \Rightarrow 20 = \dfrac{{C.P. - S.P.}}{{C.P.}} \times 100 \\
   \Rightarrow \dfrac{1}{5} = \dfrac{{C.P. - S.P.}}{{C.P.}} \\
\]
Now if C.P. is 5 then S.P. is 4 from above ratio.
But we are given that in first transaction S.P. is 18000
So to get the C.P
\[
   \Rightarrow \dfrac{5}{4} \times 18000 \\
   \Rightarrow 5 \times 4500 \\
   \Rightarrow 22500 \\
\].
This is the value of C.P. Rs.22500
Transaction 2:
In this I want to sell the A.C. but this time at a profit of 10%.
So, C.P. is the same for A.C. with profit of 10%.
Using the formula for percentage profit,
\[\% profit = \dfrac{{profit}}{{C.P.}} \times 100\]
\[
   \Rightarrow \% profit = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 \\
   \Rightarrow 10 = \dfrac{{S.P. - 22500}}{{22500}} \times 100 \\
   \Rightarrow 1 = \dfrac{{S.P. - 22500}}{{22500}} \times 10 \\
   \Rightarrow \dfrac{{22500}}{{10}} = S.P. - 22500 \\
   \Rightarrow 2250 = S.P. - 22500 \\
   \Rightarrow S.P. = 22500 + 2250 \\
   \Rightarrow S.P. = 24750 \\
\]
So the selling price for second transaction is Rs.24750.

Note: Cost of first transaction will be the same cost of A.C. during second transaction. No need to calculate other values. Assume variables instead of writing cost price and selling price every time.