Question

A container holds a mixture of Orange, Apple, and Guava juices in the ratio of 5:7:4 respectively. 24 litres of this mixture is taken out, and then 10 litres of orange juice and 6 litres of guava juice are added to the vessel. If the resultant quantity of apple juice is 14 litres more than the resultant quantity of orange juice, what was the initial quantity of mixture in the vessel (in litres)?

• A. 216
• B. 210
• C. 214
• D. 235

Answer 1

Answer:

A. 216

Let the initial quantity of the mixture be (x) litres.

The juices are in the ratio:

• Orange : Apple : Guava = 5 : 7 : 4

• Total parts = (5+7+4=16)

So initially:

• $Orange = (\frac{5x}{16})$

• $Apple = (\frac{7x}{16})$

• $Guava = (\frac{4x}{16}=\frac{x}{4})$

Step 1: Remove 24 litres of mixture

Since the mixture is removed uniformly, the ratio remains the same.

Removed:

• $Orange = (24\times\frac{5}{16}=7.5) L$

• $Apple = (24\times\frac{7}{16}=10.5) L$

• $Guava = (24\times\frac{4}{16}=6) L$

Remaining:

• $Orange = (\frac{5x}{16}-7.5)$

• $Apple = (\frac{7x}{16}-10.5)$

• $Guava = (\frac{x}{4}-6)$

Step 2: Add juices

Added:

• Orange = 10 L

• Guava = 6 L

So final quantities:

• Orange = $(\frac{5x}{16}-7.5+10=\frac{5x}{16}+2.5)$

• Apple = $(\frac{7x}{16}-10.5)$

• Guava = $(\frac{x}{4})$

Step 3: Use the given condition

Apple is 14 litres more than Orange:

• $\frac{7x}{16}-10.5=\left(\frac{5x}{16}+2.5\right)+14$
  $\frac{7x-5x}{16}=27$
  
  $\frac{2x}{16}=27$
  
  $\frac{x}{8}=27$
  

x=216