Question

65 A 40-liter mixture contains juice and water in the ratio 5:3. How much water (in liters) must be added to this mixture to change the ratio of juice to water to 2:3?

• A. 15.5 litres
• B. 22.5 litres
• C. 25 litres
• D. 30 litres

Answer 1

Answer:

B. 22.5 litres

Initial mixture = 40 L
Ratio (juice : water) = 5 : 3

Find initial quantities

Total parts = (5 + 3 = 8)

• $Juice = (\frac{5}{8} \times 40 = 25) L$

• $Water = (\frac{3}{8} \times 40 = 15) L$

  Add water

Let (x) liters of water be added.

New water = (15 + x)
Juice remains = 25

New ratio:
$\frac{25}{15 + x} = \frac{2}{3}$

Solve

• $3 \times 25 = 2(15 + x)$
  75 = 30 + 2x
  $2x = 45 \Rightarrow x = 22.5$
  

  Final Answer:

  $\boxed{22.5 \text{ liters}}$