Question

In a basket, \[\dfrac{3}{ 4 \\
    \\
}\]$th$ of the total fruits are apples, $\dfrac{2}{3}$$rd$ of the remaining are peach and the rest $300$ are oranges. Find the total number of fruits in the basket.
A) $2000$
B) $2400$
C) $3000$
D) $3600$

Answer 1

- Hint: Add all the fruits and it is equal to the total number of fruits in the basket. Firstly, let total number of fruits be x then total number of apples are $\dfrac{3}{4}x$ and total peaches are $\left( {1 - \dfrac{3}{4}} \right)\dfrac{2}{3}x$. And the total number of oranges is 300.

Complete step-by-step solution:
 According to question,
In a basket,
Let total number of fruits be $x$, $\dfrac{3}{4}$of total fruits are apples,
So, Total number of Apples $ = $ $\dfrac{3}{
  4 \\
    \\
 }$$x$
And $\dfrac{2}{3}rd$remaining are peach,
So, Total number of Peach $ = $ $\left( {1 - \dfrac{3}{4}} \right)\dfrac{2}{3}x$
 Total number of Oranges $ = $ 300
Total number of fruits in a basket $ = $total number of Apples $ + $total number of Peach $ + $total number of Oranges,
$x = \dfrac{3}{4}x + \dfrac{1}{4} \times \dfrac{2}{3}x + 300$
Simplifying the above equation,
$x = \dfrac{{9x + 12x + 3600}}{{12}}$
$12x = 11x + 3600$
On solving the above equation, we get
$x = 3600$

Therefore, the total number of fruits in the basket is equal to $3600$. So, the correct answer is option D.

Note:
Read the question properly and write all the parts that are given in the question. As in the question different conditions for fruits are given so by using these conditions to calculate the number of different fruits.