Question

If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is
A. 25%
B. \[33\dfrac{1}{3}\%\]
C. \[50\%\]
D. \[66\dfrac{2}{3}\%\]

Answer 1

Hint: Assume the cost price of single pen is x and the let the selling price of one pen be y
Then one condition is given that the cost price of 12 pens is equal to the selling price of 8 pens, it means we can write the expression \[12\times x=8\times y\]
And we know that gain percentage formula is \[\dfrac{(y-x)}{x}\times 100\]
Now just put y with respect to x in gain percentage and got the result

Complete step-by-step answer:
Given that If the cost price of 12 pens is equal to the selling price of 8 pens, to find the gain percentage.
So, let’s assume the cost price of single pen is x, it means that the cost price of 12 pen is \[12\times x\]
Similarly assume that the selling price of 8 pens is y, it means that the selling price of 8 pen is \[8\times y\]
Now it given they are equal so we can write \[12\times x=8\times y\]
\[y=\dfrac{3}{2}x....(1)\]
Now we have a relation between x and y
Now we know that formula for gain percentage is \[\dfrac{(y-x)}{x}\times 100.....(2)\]
Putting equation (1) in equation (2)
Our equation will look like \[\dfrac{(\dfrac{3}{2}x-x)}{x}\times 100=\dfrac{0.5x}{x}\times 100\]
On further solving we got 50%
Hence gain percentage is 50%,

So, the correct answer is “Option C”.

Note: If the question is like, the cost price of 8 pens is equal to the selling price of12 pens find the gain percent , then again we use the same procedure as discussed above but this time you will notice that gain percentage will be \[\dfrac{(x-\dfrac{3}{2}x)}{x}\times 100=\dfrac{-0.5x}{x}\times 100\]
-50% is the answer this time, it means our gain percentage is negative it means loss percentage is 50%