Question

If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain percent earned by the dealer.`

Answer 1

Hint: Let us assume the cost price of 1 water bottle be $x$ then the cost price of 17 water bottles is equal to $17x$. Now, it is given that the cost price of 17 water bottles is equal to the selling price of 16 water bottles so the selling price of 16 bottles is equal to $17x$ so the selling price of 1 bottle is equal to $\dfrac{17}{16}x$. To calculate the gain percent, subtract the cost price of 1 water bottle from the selling price of one water bottle and then divide this difference by the cost price of one water bottle followed by multiplication of 100.

Complete step-by-step solution -
Let us assume that the cost price (C.P.) of 1 water bottle is $x$.
Then the cost price of 17 water bottles is equal to $17x$.
It is given that the cost price of 17 water bottles is equal to the selling price (S.P.) of 16 bottles.
C.P. of 17 water bottles = S.P. of 16 water bottles
From the above, we have shown that the cost price of 17 water bottles is equal to $17x$.
C.P. of 17 water bottles = S.P. of 16 water bottles = $17x$
From the above,
S.P. of 16 water bottles = $17x$
∴ S.P. of 1 water bottle = $\dfrac{17}{16}x$
We have to find the gain percent which we know the formula for gain percent is:
$\text{Gain percent =}\dfrac{\left( \text{S}\text{.P}\text{. - C}\text{.P}\text{.} \right)}{\text{C}\text{.P}\text{. }}\times 100$
The gain percent on 1 bottle is calculated by subtracting C.P. of 1 water bottle from the S.P. of 1 water bottle and then divide this subtraction by C.P. of 1 water bottle and further multiply by 100.

$\text{Gain percent =}\dfrac{\left( \text{S}\text{.P}\text{. - C}\text{.P}\text{.} \right)\text{ of 1 water bottle}}{\text{C}\text{.P}\text{. of 1 water bottle}}\times 100$
(S.P. – C.P.) of 1 water bottle$=\dfrac{17}{16}x-x=\dfrac{x}{16}$.
And C.P. of 1 water bottle = $x$
Substituting these values in the gain percent formula we get,
$\begin{align}
  & \text{Gain percent =}\dfrac{\dfrac{x}{16}}{x}\times 100 \\
 & \Rightarrow \text{Gain percent =}\dfrac{1}{16}\times 100=6.25 \\
\end{align}$
From the above solution, the gain percent we have calculated is $6.25\%$.
 Hence, the gain per cent of a dealer is $6.25\%$.

Note: At first, while reading the question you might think that we should find the gain percent for 16 bottles or 17 bottles. But in the above solution we have found the gain percent for 1 water bottle. The answer won’t change if you find the gain percent for 16 bottles or 17 bottles because when you see the formula of gain percent which is:
$\text{Gain percent =}\dfrac{\left( \text{S}\text{.P}\text{. - C}\text{.P}\text{.} \right)\text{ of 1 water bottle}}{\text{C}\text{.P}\text{. of 1 water bottle}}\times 100$
In the above formula, if instead of 1 water bottle you will find for 16 or 17 bottles then in both the numerator and denominator we have to multiply by either 16 or 17 which will be cancelled out from the numerator and denominator and the answer would be the same in both the conditions.
There is a benefit of finding gain percent for 1 water bottle as it will reduce the calculations also.