Question

A flower girl makes a profit of 45% by selling flowers at a certain price. If she charges ₹. 1 more on each flower, she would gain 70%. Find the original price/ flower at which she sold the flower.
A.₹\[4.00\]
B.₹\[5.80\]
C.₹\[5.40\]
D.₹\[6.00\]
E.₹\[6.40\]

Answer 1

Hint: Here, we will find the selling price of a flower. We will use the selling price using the profit percentage formula and we will arrive at two equations with the given and by equating and substituting these equations, we will find the cost price and selling price of a flower. Thus, we will find the original price at which she sold the flower.

Formula Used: Selling price is given by the formula \[S.P. = \left( {\dfrac{{100 + Gain\% }}{{100}}} \right) \times C.P.\]

Complete step-by-step answer:
Let \[x\] be the cost price of a flower and \[y\] be the selling price of a flower.
We are given that a flower girl makes a profit of 45% by selling flowers at a certain price.
Selling price is given by the formula \[S.P. = \left( {\dfrac{{100 + Gain\% }}{{100}}} \right) \times C.P.\]
\[ \Rightarrow \] So, we get \[y = \left( {\dfrac{{100 + 45}}{{100}}} \right) \times x\]
\[ \Rightarrow \] \[y = \left( {\dfrac{{145}}{{100}}} \right) \times x\]
By simplifying, we get
\[ \Rightarrow \] \[y = \left( {\dfrac{{29}}{{20}}} \right) \times x\] …………………………………………………………………………………………………\[\left( 1 \right)\]
We are also given that if she charges ₹. 1 more on each flower, she would gain 70%.
Selling price is given by the formula \[S.P. = \left( {\dfrac{{100 + Gain\% }}{{100}}} \right) \times C.P.\]
\[ \Rightarrow \] So, we get \[y + 1 = \left( {\dfrac{{100 + 70}}{{100}}} \right) \times x\]
\[ \Rightarrow \] \[y + 1 = \left( {\dfrac{{170}}{{100}}} \right) \times x\]
By simplifying, we get
\[ \Rightarrow \] \[y + 1 = \left( {\dfrac{{34}}{{20}}} \right) \times x\] …………………………………………………………………………………………………\[\left( 2 \right)\]
By substituting equation\[\left( 1 \right)\] in equation \[\left( 2 \right)\], we get
\[ \Rightarrow \] \[\dfrac{{29}}{{20}}x + 1 = \left( {\dfrac{{34}}{{20}}} \right) \times x\]
By rewriting the equation, we get
\[ \Rightarrow \] \[\dfrac{{34}}{{20}}x - \dfrac{{29}}{{20}}x = 1\]
By subtracting the like terms, we get
\[ \Rightarrow \] \[\dfrac{5}{{20}}x = 1\]
By rewriting the equation, we get
\[ \Rightarrow \] \[5x = 20\]
Dividing by 5 on both the sides, we get
\[ \Rightarrow \] \[x = 4\]
By substituting \[x = 4\] in equation \[\left( 1 \right)\], we get
\[ \Rightarrow \] \[y = \left( {\dfrac{{29}}{{20}}} \right) \times 4\]
By dividing the term, we get
\[ \Rightarrow \] \[y = \left( {\dfrac{{29}}{5}} \right)\]
\[ \Rightarrow \] \[y = 5.80\]
Thus, the selling price of a flower is ₹\[5.80\] and the cost price of a flower is ₹\[4.00\]
Therefore, the original price at which she sold a flower is ₹\[5.80\].
Thus Option(B) is the correct answer.

Note: We know that the cost price is the price of an item at which an item is bought. The selling price is the price of an item at which an item is sold. If the selling price is greater than the cost price, then there is a profit. If the selling price is less than the cost price, then there is a loss. Profit or loss percentage is calculated only for the same number of items. Both the percentages are calculated over the cost price of an item. We know that we have many selling price formulas but we prefer the formula which is suitable with the given parameters.