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Hint: Assume a variable x that represents the number of oranges that were bought by the fruit vendor. Since the number of oranges bought is equal to the number of bananas bought, the number of bananas bought is also equal to x. If we have an amount of Rs y and we make z % of profit on it then, the profit made by us on Rs y is equal to $\dfrac{yz}{100}$. Using this, we can solve this question.

Complete step-by-step answer:

Before proceeding with the question, we must know the formulas that will be required to solve this question.

In profit and loss, if we have an amount Rs y and If we are making a Z% profit on this amount, then the profit in rupees we are making on this amount is equal to Rs $\dfrac{yz}{100}$ . . . . . . . . (1)

In the question, we are given that the fruit vendor buys some oranges at the rate of Rs 5 per orange and an equal number of bananas at the rate of Rs 2 per banana. It is given that he is making a profit of 20 % on the oranges and 15 % profit on bananas. Also, when he sold all his fruits in a day, he made a total profit of Rs 390. We are required to find the number of oranges he purchased.

Let us assume that he bought x oranges and x bananas. Since the rate of oranges is Rs 5 per orange and the rate of bananas is Rs 2 per banana, he spent Rs 5x on oranges and Rs 2x on bananas.

It is given that he makes 20 % on oranges. So, from formula (1), the total profit on oranges is $\dfrac{20\left( 5x \right)}{100}=x$.

Also, it is given that he makes 15 % on bananas. So, from formula (1), the total profit on bananas is $\dfrac{15\left( 2x \right)}{100}=\dfrac{3x}{10}$.

So, the total profit he made in the day is $x+\dfrac{3x}{10}=\dfrac{13x}{10}$. Since this profit is equal to Rs 390, we can say,

$\begin{align}

& \dfrac{13x}{10}=390 \\

& \Rightarrow x=300 \\

\end{align}$

Hence, the number of oranges purchased is 300.

Note: It is an easy question which can be solved using the basic knowledge of profit and loss. So, the only possible mistake one can make in this question is calculation mistake. So, one must be careful while doing calculations in such types of questions.

Complete step-by-step answer:

Before proceeding with the question, we must know the formulas that will be required to solve this question.

In profit and loss, if we have an amount Rs y and If we are making a Z% profit on this amount, then the profit in rupees we are making on this amount is equal to Rs $\dfrac{yz}{100}$ . . . . . . . . (1)

In the question, we are given that the fruit vendor buys some oranges at the rate of Rs 5 per orange and an equal number of bananas at the rate of Rs 2 per banana. It is given that he is making a profit of 20 % on the oranges and 15 % profit on bananas. Also, when he sold all his fruits in a day, he made a total profit of Rs 390. We are required to find the number of oranges he purchased.

Let us assume that he bought x oranges and x bananas. Since the rate of oranges is Rs 5 per orange and the rate of bananas is Rs 2 per banana, he spent Rs 5x on oranges and Rs 2x on bananas.

It is given that he makes 20 % on oranges. So, from formula (1), the total profit on oranges is $\dfrac{20\left( 5x \right)}{100}=x$.

Also, it is given that he makes 15 % on bananas. So, from formula (1), the total profit on bananas is $\dfrac{15\left( 2x \right)}{100}=\dfrac{3x}{10}$.

So, the total profit he made in the day is $x+\dfrac{3x}{10}=\dfrac{13x}{10}$. Since this profit is equal to Rs 390, we can say,

$\begin{align}

& \dfrac{13x}{10}=390 \\

& \Rightarrow x=300 \\

\end{align}$

Hence, the number of oranges purchased is 300.

Note: It is an easy question which can be solved using the basic knowledge of profit and loss. So, the only possible mistake one can make in this question is calculation mistake. So, one must be careful while doing calculations in such types of questions.

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