Question

60% of the fruits were apples while the rest we oranges and pears. 30%
of the oranges and pears were pears. There were 48 fewer oranges than
apples. How many fruits were there altogether?

Answer 1

Given:

60% of the fruits were apples while the rest we oranges and pears.

30%  of the oranges and pears were pears.

There were 48 fewer oranges than  apples.

To find:

How many fruits were there altogether?

Solution:

Let's assume "x" represents the total no. of fruits.

60% of the fruits were apple

So, no. of apples = $\frac{60}{100}\times x = \frac{3x}{5}$

∴ The remaining no. of pears and oranges were = $x - \frac{3x}{5} = \frac{5x - 3x}{5} = \frac{2x}{5}$

30% of the pears & oranges are pears

So, no. of pears = $\frac{30}{100}\times \frac{2x}{5} = \frac{3x}{25}$

There were 48 fewer oranges than  apples

So, no. of oranges = no. of apples - 48

i.e., no. of oranges = $\frac{3x}{5} - 48$

Therefore, we can form an equation as:

$\frac{3x}{5} + \frac{3x}{25} + \frac{3x}{5} - 48 = x$

$\implies \frac{15x\:+3x\:+\:15x\:-\:1200}{25} = x$

$\implies 15x\:+3x\:+\:15x\:-\:1200 = 25x$

$\implies 33x - 1200 = 25x$

$\implies 8x = 1200$

$\implies x = \frac{1200}{8}$

$\implies \bold{x = 150}$

Thus, there were altogether 150 fruits.

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