Container P contains a mixture of apple juice and grape juice in the ratio of 4 : 1 respectively. 30 liters of the mixture is taken out from container P and poured into container Q, which contains x liters of apple juice and 24 liters of grape juice. If the ratio of apple juice to grape juice in the final mixture in container Q is 3 : 2, then find the value of x.

The correct option is 21.

Given:
Ratio of apple juice to grape juice in Container P = 4 : 1
Quantity of mixture taken out from Container P = 30 liters
Initial quantity of apple juice in Container Q = x liters
Initial quantity of grape juice in Container Q = 24 liters
Final ratio of apple juice to grape juice in Container Q = 3 : 2

Step 1: Find the quantity of apple juice and grape juice in the 30 liters drawn from Container P.

Total parts in the ratio = 4 + 1 = 5 parts

Quantity of apple juice taken out:

$\text{Apple juice}=\frac{4}{5}\times 30=24\text{liters}$

Quantity of grape juice taken out:

$\text{Grape juice}=\frac{1}{5}\times 30=6\text{liters}$

Step 2: Calculate total quantities in Container Q after adding 30 liters.

New quantity of apple juice in Container Q = (x + 24) liters
New quantity of grape juice in Container Q = 24 + 6 = 30 liters

Step 3: Solve for x using the final ratio.

The ratio of apple juice to grape juice in Container Q becomes 3 : 2:

$\frac{x+24}{30}=\frac{3}{2}$

Cross-multiplying both sides:

$2\times (x+24)=3\times 30$

$2x+48=90$

$2x=90-48$

$2x=42$

$x=21$

Therefore, the value of x is 21.