7 liters of milk and 3 liters of water is mixed in an empty bucket 'P'. In other empty bucket 'Q' six liters of milk is mixed in 1 liter of water. 3 liters of mixture 'P' and 4 liters of mixture from bucket'Q' are mixed in an empty bucket 'R'. What is the quantity of water (in liters) in bucket 'R' ?

Correct option is B

Given:

Bucket 'P' contains 7 liters of milk and 3 liters of water.

Bucket 'Q' contains 6 liters of milk and 1 liter of water.

From bucket 'P', 3 liters of the mixture is taken.

From bucket 'Q', 4 liters of the mixture is taken.

Concept Used:

The amount of water in a mixture is proportional to the quantity taken from the total mixture.

Solution:

Water content in bucket 'P' =$$\frac{3}{10}$$​ of the total mixture (since 7 + 3 = 10) .

Water content in bucket 'Q' $$= \frac{1}{7}$$​ of the total mixture (since 6 + 1 = 7 ).

For bucket 'P':

In 3 liters of mixture taken from bucket 'P', the amount of water is:

​$$\frac{3}{10} \times 3 = 0.9 \text{ liters of water}.$$​​

For bucket 'Q':

In 4 liters of mixture taken from bucket 'Q', the amount of water is:

​$$\frac{1}{7} \times 4 = \frac{4}{7} \approx 0.571 \text{ liters of water}.$$​​

Total water in bucket 'R':

Total water in bucket 'R' is the sum of water from both mixtures:
0.9 + 0.571 = 1.471 liters of water.

1.471 = 1 +$$\frac{33}{70}.$$​​

Thus, the quantity of water in bucket 'R' is 1$$\frac{33}{70}.$$​ liters.

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