Question

A fruit seller sells 4 oranges for\[Rs.3\], gaining \[50\% \]. The number of oranges bought and sold to gain \[Rs.24\].

Answer 1

Hint: The given of this question percentage of gain. First of all, identify the selling price (S.P.) of one orange. Now calculate the cost price (C.P.) of 4 oranges and then the cost price of one orange. The next step is to calculate the profit made by selling one orange. Then you can find the number of oranges which give a profit of \[Rs.{\text{ }}24\].

Complete step-by-step answer:
Fruit seller sells 4 oranges for \[Rs.3\], gaining \[50\% \].
We have to find the number of oranges bought and sold to gain \[Rs.{\text{ }}24\].
From the given information in the question,
Selling price of 4 oranges = Rs. \[3\]
Selling price of 1 orange = Rs. \[\dfrac{3}{4}\]
Gain percentage = \[50\% \]

We know that, Cost price\[ = \dfrac{{({\text{S}}{\text{.P}} \times 100)}}{{(100 + {\text{gain}}\% )}}\]

Calculating the cost price of 4 oranges, by using the data Selling price = \[3\]; Gain = \[50\% \] we have

Cost price\[{\text{ = }}\dfrac{{(3 \times 100)}}{{(100 + 50)}}\]

After simplification, we get

Cost price \[ = \dfrac{{300}}{{150}} = 2\]

Cost price of 4 oranges\[ = {\text{ }}Rs.2\]
Cost price of 1 oranges\[ = \dfrac{2}{4} = {\text{ }}Rs.\dfrac{1}{2}\]
Therefore,
\[{\text{Profit made by selling one orange = Selling price of 1 orange - Cost price of 1 orange}}\]
Profit made by selling one orange\[{\text{ = }}\dfrac{{\text{3}}}{{\text{4}}}{\text{ - }}\dfrac{{\text{1}}}{{\text{2}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{4}}}{\text{ = Rs}}{\text{.}}\,{\text{0}}{\text{.25}}\]
Given that the gain is \[Rs.{\text{ }}24\]
\[{\text{The number of oranges sold to gain Rs}}{\text{.24 = }}\dfrac{{{\text{given gain rupees}}}}{{{\text{gain of one orange}}}} = \dfrac{{24}}{{0.25}} = 96\]
So, the number of oranges sold to gain \[Rs.{\text{ }}24\] is 96.

Note: You should consider the formula to find out C.P in the case of gain as the formula changes in the case of loss. Don’t confuse between the C.P and S.P of 1 and 4 oranges. By following the above step by step process, you can get the solution with no doubts.