Question

A sells an article to B for Rs.45000 losing \[10\%\] in the transaction. B sells it to C at a price which would have given a profit of \[10\%\] to A. By what percent does B gain?
(A) \[22\%\]
(B) \[20\%\]
(C) \[24\%\]
(D) \[26\%\]

Answer 1

Hint: We are given that A sells an article to B with a loss of \[10\%\] for Rs.45000. B further sells it for a profit of \[10\%\]. And we are asked to find the percentage by which B gained. Firstly, we will find the C.P of the article for A using the formula, \[C.P=\dfrac{100}{100-Loss\%}\times S.P\]. Then, we know that the S.P for A will be the C.P for B. Next, we will find the S.P for B and it is given that S.P for B would have given \[10\%\] profit to A, we will use the formula, \[S.P=\dfrac{100+Gain\%}{100}\times C.P\]. Here, C.P is the same as for A.
Then, we will calculate the profit and the profit percentage using the formula, \[profit\%=\dfrac{profit}{C.P}\times 100\]. Hence, we will have the required gain percent.

Complete step-by-step solution:
According to the given question, we are given that A sells an article to B with a loss of \[10\%\] for Rs.45000. B further sells it for a profit of \[10\%\]. And we are asked to find the percentage by which B gained.
First of all, we will find the C.P for A and we will use the formula,
\[C.P=\dfrac{100}{100-Loss\%}\times S.P\]
Substituting the values in the above expression we get,
\[\Rightarrow C.P=\dfrac{100}{100-10}\times 45000\]
Solving further, we get,
\[\Rightarrow C.P=\dfrac{100}{90}\times 45000\]
\[\Rightarrow C.P=\dfrac{10}{9}\times 45000\]
\[\Rightarrow C.P=10\times 5000\]
We have the value of C.P as,
\[\Rightarrow C.P=Rs.50000\]
Now, we know that the S.P of the article for A will be C.P of the article for B and which is,
S.P of the article for A = C.P of the article for B = Rs.45000
Now, we will have to find the S.P of the article for B.
It is given that B sells it to C at a price that would have caused a profit of \[10\%\] to A, so we will use the formula,
\[S.P=\dfrac{100+Gain\%}{100}\times C.P\]
Here, we will take the C.P as the C.P of the article for A, and we get,
\[\Rightarrow S.P=\dfrac{100+10}{100}\times 50000\]
Solving further, we get,
\[\Rightarrow S.P=\dfrac{110}{100}\times 50000\]
\[\Rightarrow S.P=11\times 5000\]
\[\Rightarrow S.P=Rs.55000\]
Now that we have the C.P and the S.P of the article for B, next, we will find the profit and we have,
\[profit=S.P-C.P\]
\[\Rightarrow profit=55000-45000\]
\[\Rightarrow profit=10000\]
Calculating the profit percentage now, we have,
\[profit\%=\dfrac{profit}{C.P}\times 100\]
Substituting the values in the above expression, we have,
\[\Rightarrow profit\%=\dfrac{10000}{45000}\times 100\]
\[\Rightarrow profit\%=\dfrac{1000}{45}\]
We get the percentage gain as,
\[\Rightarrow profit\%=\dfrac{200}{9}=22.22\%\]
\[\Rightarrow profit\%\simeq 22\%\]
Therefore, the correct answer is (A) \[22\%\].

Note: The substitution of values in the formulae should be carefully done and without any mistaking. Also, while calculating the S.P of the article for B we used the value of C.P of the article for A as it was stated in the question for B with respect to A’s. so, accordingly the appropriate values have to be put, else the answer will be something else.