Question

By selling a bouquet for $Rs.345$ a florist gains $15\% $. At what price should he sell, it gains $25\% $?

Answer 1

Hint: Selling Price $ = $Standard Price$ + $ Profit
First, we need to solve the given problem to find the gain percentage. Once we found the gain percentage, we will apply it to the formula given above to find the selling price. Since the question itself mentions the gain percentage, so that only we applied it directly.

Complete step-by-step solution:
From the given problem, to find the selling price with the profit of $25$% from the standard price, first we have to find the standard price of the bouquet.
First, we are going to find the standard price,
Using the above hint,
Selling Price $ = $Standard Price$ + $ Profit.
Here, from the given problem we are given that the Selling price is $345$ and the profit is $15$% of the standard price. Let us assume that $x$ is the standard price.
Now selling price $ = 345$,
standard price$ = x$
Profit $ = $$\left( {\dfrac{{15}}{{100}}} \right)$$x$
By substituting the values, we can get that
$345 = x + \left( {\dfrac{{15}}{{100}}} \right)$$x$
By taking $x$ in common from the right hand side of the above equation, we will get
$345 = x\left( {1 + \dfrac{{15}}{{100}}} \right)$
By doing some calculations, we will get
$345 = x\left( {\dfrac{{115}}{{100}}} \right)$
By cancelling $5$ from the right hand side we will get
$345 = x\left( {\dfrac{{23}}{{20}}} \right)$
Now, by multiplying $\left( {\dfrac{{20}}{{23}}} \right)$ in both sides of the above equation, we will get
$\left( {\dfrac{{20}}{{23}}} \right)345 = x\left( {\dfrac{{20}}{{23}}} \right)\left( {\dfrac{{23}}{{20}}} \right)$
By doing some calculations on both sides, we will get
$20\left( {\dfrac{{345}}{{23}}} \right) = x$
By dividing $345$ by $23$ in the above equation we will get
$x = 20\left( {15} \right)$
By multiplying we will get,
$x = 300$.
Therefore, the standard price of the bouquet is Rs.$300$.
Now, we are going to find the selling price for the profit of $25$%.
From the hint, we know that,
Selling Price $ = $Standard Price$ + $ Profit
For the selling price for the profit of $25$% is
Selling price$ = 300 + \left( {\dfrac{{25}}{{100}}} \right)300$
By taking $300$ from the above equation we will get,
Selling price$ = 300\left( {1 + \dfrac{1}{4}} \right)$
Selling price$ = 300\left( {\dfrac{5}{4}} \right)$
Therefore, Selling Price$ = 375$.
Selling price for the profit of $25$% is Rs.$375$

Note: Also, we can make use of the formulas like $G\% = \dfrac{{SP - CP}}{{CP}} \times 100$ where G is the gain percentage, SP is the selling price and CP is the cost price. So, we can also use the formula to find the gain percentage. Note that the gain percentage cannot be negative, because it was gaining positive values from the given cost.