Question

A Smoothie contains feruit.
extracts and yoguent in
the ratio 5.1. on adding 5
litres of yogurt the ratio
of fruit extract to yogurt
becomes 5:2. what is the
quantity of fruit extract en
the smoothie?​

Answer 1

Given :  A Smoothie contains fruit. extracts and yoguett in the ratio 5.1. on adding 5 litres of yogurt the ratio of fruit extract to yogurt becomes 5:2

To find : what is the quantity of fruit extract and the smoothie

Solution:

Let say Fruit extract  = 5A  Litre

Then Yoghurt = A Litre

Total mixture = 6A Litre

5 Litre Yoghurt added

hence Yogurt = A + 5

5A /( A + 5)  = 5/2

=> 10A = 5A + 25

=> 5A = 25

original Fruit extract = 25 Litre

Yogurt = 5 Litre

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Answer 2

Given:

The ratio of the fruit extract and yogurt in the smoothie = 5:1

5 litres of yogurt is added in the smoothie

The new ratio of fruit extract to yogurt = 5:2

To find:

The quantity of fruit extract in  the smoothie

Solution:

Let's assume from the given original ratio of fruit and yogurt,

"5x" → quantity of fruit extract in the smoothie

"x" → quantity of yogurt in the smoothie

5 litres of yogurt is added to the smoothie

∴ The new quantity of yogurt in the smoothie becomes = (x + 5) litres

Now, according to the question we can form an equation as,

$\frac{5x}{(x\:+\:5)} = \frac{5}{2}$

⇒ $2\:\times\:5x = 5\:\times\:(x\:+\:5)$

⇒ $10x = 5x + 25$

⇒ $10x \:-\:5x = 25$

⇒ $5x\:=\: 25$

⇒ $x = 5\: litres$

∴ 5x = 5 × 5 = 25 litres ← quantity of fruit extract

Thus, the quantity of fruit extract in the smoothie is 25 litres.

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