Question

Some articles were brought at $6$ articles for $Rs.5$ and sold at $5$ articles for $Rs.6$ Gain percent is?
(A) $33\%$
(B) $33\dfrac{1}{3}\%$
(C) $35\%$
(D) $44\%$

Answer 1

Hint: For answering this question we will consider the given information in the question that is some articles were bought at $6$articles for $Rs.5$ and sold at $5$ articles for $Rs.6$ . And derive the cost price and selling price of individual articles. Then we will calculate the Gain per cent using the formula stated as $\dfrac{\text{selling price-cost price }}{\text{cost price}}\times 100\%$.

Complete step-by-step solution
Now consider the question it is given that the articles are brought at $6$ articles for $Rs.5$ and sold at $5$ articles for $Rs.6$.
As it is given that the cost price of $6$ articles is $Rs.5$ so we will have the cost price of one article is $Rs.\dfrac{5}{6}$.
And similarly, we can extract the selling price of one article is $Rs.\dfrac{6}{5}$.
From the basic concept it is given that the gain per cent is given as $\dfrac{\text{selling price-cost price }}{\text{cost price}}\times 100\%$
In this case it can be given as $\dfrac{\left( \dfrac{6}{5}-\dfrac{5}{6} \right)}{\left( \dfrac{5}{6} \right)}\times 100$ .
By simplifying this we will have
$\begin{align}
  & \dfrac{\left( \dfrac{6}{5}-\dfrac{5}{6} \right)}{\left( \dfrac{5}{6} \right)}\times 100 \\
 & \Rightarrow \dfrac{\left( \dfrac{36-25}{30} \right)}{\left( \dfrac{5}{6} \right)}\times 100 \\
 & \Rightarrow \dfrac{\left( \dfrac{11}{30} \right)}{\left( \dfrac{5}{6} \right)}\times 100 \\
\end{align}$ .
By further simplifying this we will have
$\begin{align}
  & \Rightarrow \left( \dfrac{11}{30} \right)\times \left( \dfrac{6}{5} \right)\times 100 \\
 & \Rightarrow \dfrac{11\times 6\times 2}{3}=44\% \\
\end{align}$.
Therefore we can conclude that the Gain percent when some articles are brought at $6$ articles for $Rs.5$ and sold at $5$ articles for $Rs.6$ is $44\%$
Hence option D is correct.

Note: While answering questions of this type we should perform the calculations carefully. The important fact is that the Gain percent is given as $\dfrac{\text{selling price-cost price }}{\text{cost price}}\times 100\%$ and the loss per cent is given as $\dfrac{\text{cost price - selling price }}{\text{cost price}}\times 100\%$ . If we had made a mistake and considered the cost price of one article as $Rs.\dfrac{8}{9}$. Then we will have Gain percent as $35\%$ which implies option C as correct which is wrong.