Question

IF the CP of 6 articles is equal to the SP of 4 articles, find the gain percent.

Answer 1

Hint: To solve this question, we will, first of all, assume a variable for the cost price of an article and then calculate the SP in terms of that variable. Finally, we will use the formula of gain and gain percent as Gain = SP – CP and \[\text{Gain Percent}=\dfrac{\text{Gain}}{CP}\times 100.\]

Complete step-by-step answer:
We are given that CP (cost price) of 6 articles is equal to the SP (selling price of 1 of 4 articles). So, let us assume the cost price of one article to be Rs. x. Then the cost price of 6 articles can be calculated by multiplying 6 by x. Hence, the cost price of the 6 articles is 6x. Similarly, the cost price of the 4 articles would be 4x. Now, because it is given that CP of 6 articles is equal to SP of 4 articles, we can write
\[\Rightarrow \text{CP of 6 articles}=6x=\text{SP of 4 articles}\]
\[\Rightarrow \text{SP of 4 articles}=6x\]
Now, we will finally calculate the gain by using the formula as
\[\text{Gain}=SP-CP\]
where SP and CP are taken from 4 articles. We know that SP of 4 articles is 6x and CP of 4 articles is 4x.
\[\Rightarrow \text{Gain}=SP-CP\]
\[\Rightarrow \text{Gain}=6x-4x\]
Also, the gain percent can be calculated by using the formula,
\[\text{Gain Percent}=\dfrac{\text{Gain}}{CP}\times 100\]
\[\Rightarrow \text{Gain Percent}=\dfrac{6x-4x}{4x}\times 100\]
Solving further, we have,
\[\Rightarrow \text{Gain Percent}=\dfrac{\left( 6-4 \right)x}{4x}\times 100\]
\[\Rightarrow \text{Gain Percent}=\dfrac{2x}{4x}\times 100\]
\[\Rightarrow \text{Gain Percent}=\dfrac{1}{2}\times 100\]
\[\Rightarrow \text{Gain Percent}=50\text{ Percent}\]
Hence, the gain percent is calculated by 50 %, which is our required result.

Note: We can also solve by assuming the SP of one article to be some variable and then cancelling in the formula of gain percent, it would be tough as we have the CP (cost price) as the denominator in the formula of gain percent. So, it is better to solve by assuming a variable for cost price (CP) of an article apart from assuming an SP (selling price) of an article.