Question

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then value is x is
(a) 15
(b) 16
(c) 18
(d) 25

Answer 1

Hint: We will first assume the cost price of each article. Then we will find the selling price of each article with 25% profit. This equation would involve x. So we can find x from that equation.

Complete step-by-step answer:
We will assume that the cost price of each article is 1 unit. Thus the total cost price would be \[20\times 1=20\] . Now on each article there should be a profit of 25%. So we will calculate what the price of each article with 25% profit will be if all those x articles are sold at 20 units. This is because the cost price of 20 articles is the same as the selling price of x articles.
Therefore, the price of each article if x articles are sold for 20 units will be \[\dfrac{20}{x}\] .
Now the profit should be 25%. So the cost of each article would be \[\left( 1+\dfrac{25}{100} \right)\times 1\]
So equating these two we would get,
\[\dfrac{20}{x}=\left( 1+\dfrac{25}{100} \right)\times 1\]
Taking LCM and solving we would get,
\[\begin{align}
  & \dfrac{20}{x}=\left( \dfrac{100+25}{100} \right)\times 1 \\
 & \dfrac{20}{x}=\left( \dfrac{125}{100} \right) \\
\end{align}\]
Cancelling the common factors, we will get,
\[\dfrac{4}{x}=\dfrac{1}{4}\]
Cross-multiplying we get,
x=16.
Thus option(b) is correct.

Note: Please be careful while reading and understanding the question. There are chances that we may assume the cost price of one article is equal to the selling price of each article (let us assume 1 unit). If we do so, we would 20 as the total selling price and x as the total cost price. Then we will apply the profit formula,
\[profit=\dfrac{TSP-TCP}{TCP}\times 100\]
Then substituting the TSP as x, TCP as 20 and profit as 25 we would get x as 25 which would be wrong.