Question

By selling a bouquet for Rs. 322, a florist gains $15\%$. At what price should he sell it to gain $25\%$?

Answer 1

Hint: Let us assume that the cost price (C.P.) of bouquet be x and the selling price (S.P.) of bouquet is already given as Rs. 322 with the gain of $15\%$. We know that, $Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100$ substituting the value of S.P. as 322 and gain% as $15\%$ we can get the value of C.P. which we have assumed as x.
Now, we have found the value of x and new gain is given as $25\%$ and cost price remains the same i.e. Rs. 322 substituting all these values in the formula of $gain\%$ we can find the new selling price.

Complete step-by-step solution -
The selling price (S.P.) of the bouquet is given as Rs. 322 with the gain of $15\%$.
Let us assume that the C.P. of the bouquet is Rs. x.
We know the formula for $gain\%$ as:
$Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100$
Substituting the value of S.P. as Rs. 322, gain as $15\%$ and C.P. as x in the above equation we get,
$15=\dfrac{322-x}{x}\times 100$
Dividing 100 on both the sides of the above equation we get,
$\begin{align}
  & \dfrac{15}{100}=\dfrac{322-x}{x} \\
 & \Rightarrow 0.15=\dfrac{322-x}{x} \\
\end{align}$
On cross – multiplication of the above equation we get,
$0.15x=322-x$
Adding x on both the sides of the above equation we get,
$\begin{align}
  & 1.15x=322 \\
 & \Rightarrow x=\dfrac{322}{1.15} \\
 & \Rightarrow x=280Rs. \\
\end{align}$
From the above, we have calculated the C.P. of the bouquet as Rs. 280.
Now, we have to find the selling price of the bouquet when the gain changes to $25\%$. We are going to substitute the value of C.P. as Rs. 280, gain as $25\%$ in the formula of $gain\%$ that we have shown above.
$\begin{align}
  & Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100 \\
 & \Rightarrow 25=\dfrac{S.P.-280}{280}\times 100 \\
\end{align}$
Dividing 100 on both the sides of the equation we get,
$\begin{align}
  & \dfrac{25}{100}=\dfrac{S.P.-280}{280} \\
 & \Rightarrow \dfrac{1}{4}=\dfrac{S.P.-280}{280} \\
\end{align}$
On cross – multiplying the above equation we get,
$\begin{align}
  & 280=4\left( S.P. \right)-1120 \\
 & \Rightarrow 4\left( S.P. \right)=1120+280 \\
 & \Rightarrow 4\left( S.P. \right)=1400 \\
\end{align}$
Dividing 4 on both the sides of the above equation we get,
$\begin{align}
  & S.P.=\dfrac{1400}{4} \\
 & \Rightarrow S.P.=350 \\
\end{align}$
From the above, the new selling price with $25\%$ gain is Rs. 350.
Hence, the C.P. of the bouquet is Rs. 280 and the new selling price with a gain of $25\%$ is Rs. 350.

Note: Be careful in writing the formula of $gain\%$. In the formula of $gain\%$,
$Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100$
The mistake that could be possible is writing a positive sign in place of the negative sign in the numerator and the order of S.P. and C.P. written in the above formula.
You can remember the above formula as gain will happen when we sell something with the greater value as compared to the cost price and as $gain\%$ cannot be negative so S.P. will come first so the cost price will come with a negative sign.