Question

On selling a bat for Rs.100, a man gains Rs.20. His gain % is

Answer 1

Hint: Let us assume the price of the bat is equal to P, the gain gained by the man is equal to G and the gain percentage is equal to A., then we get \[\Rightarrow A=\dfrac{G}{P}\times 100\]. By using this concept, we can find the value of gain percentage by using the price of the bat and the gain of the bat after selling.

Complete step-by-step answer:
From the question, it is given that the price of the bat is equal to Rs.100. It is also given that the gain by the man is equal to Rs.20.
We know that the gain percentage is equal to the ratio of the amount of gain obtained by selling the object to the cost price of the object.
Let us assume the price of the bat is equal to P, the gain gained by the man is equal to G and the gain percentage is equal to A., then we get
\[\Rightarrow A=\dfrac{G}{P-G}\times 100\].
Let us consider
\[\Rightarrow A=\dfrac{G}{P-G}\times 100......(1)\]
From the question, we can say that the value of P is equal to 100, the value of G is equal to 20.
 \[\begin{align}
  & \Rightarrow P=100....(2) \\
 & \Rightarrow G=20......(3) \\
\end{align}\]
Now we will substitute equation (2) and equation (3) in equation (1), then we get
\[\begin{align}
  & \Rightarrow A=\dfrac{20}{100-20}\times 100 \\
 & \Rightarrow A=\dfrac{20}{80}\times 100 \\
 & \Rightarrow A=25\%...(4) \\
\end{align}\]
From equation (4), it is clear that the value of A is equal to $25\%$. So, we can say that the gain percentage is equal to $25\%$ if the selling price of bat is equal to 100 and the gain is equal to 20.

Note: Some students may have a misconception that if the price of the bat is equal to P, the gain gained by the man is equal to G and the gain percentage is equal to A., then we get
\[\Rightarrow A=\dfrac{P-G}{G}\times 100.....(1)\].
If this misconception is followed, then we get
From the question, we can say that the value of P is equal to 100, the value of G is equal to 20.
 \[\begin{align}
  & \Rightarrow P=100....(2) \\
 & \Rightarrow G=20......(3) \\
\end{align}\]
Now we will substitute equation (2) and equation (3) in equation (1), then we get
\[\begin{align}
  & \Rightarrow A=\dfrac{100-20}{20}\times 100 \\
 & \Rightarrow A=\dfrac{80}{20}\times 100 \\
 & \Rightarrow A=400...(4) \\
\end{align}\]
From equation (4), it is clear that the value of A is equal to 400. So, we can say that the gain percentage is equal to 20 if the price of bat is equal to 100 and the gain is equal to 400. But we know that the percentage is equal to 25. So, this misconception should be avoided.