Question

In a 56 lilters mixture of milk and water, the ratio of milk to water is 5 : 2. In order to make the ratio of milk to water 7 : 2, some quantity of milk is to be added to the mixture. The quantity of the milk present in the new mixture will be:

• A. 40 liters
• B. 16 liters
• C. 56 liters
• D. 48 liters

Answer 1

Answer:

C. 56 liters

Solution:

Given:

In 56 liters, 

The ratio of milk to water is 5 : 2

Calculation:

The ratio of milk to water is 5 : 2

⇒ Milk in the total mixture = $\frac{5}{7}$ of the total mixture

⇒ Quantity of Milk $=\frac{5}{7}\times{56}$

⇒ Quantity of Milk = 40 liters

Quantity of Water = Total mixture – Quantity of Milk

⇒ Quantity of Water = 56 – 40

⇒ Quantity of Water = 16 liters

Now, in the final mixture,

the ratio of milk to water 7 : 2

⇒ Water in the final mixture $=\frac{2}{9}$ of the total mixture

⇒ $16 = \frac{2}{9}\times{Total mixture}$

⇒ Total mixture $=\frac{(16\times{9})}{2}$

⇒ Total mixture = 72 liters

Quantity of Milk = Total mixture – Quantity of Water

⇒ Quantity of Milk = 72 –  16

⇒ Quantity of Milk = 56 liters

∴ The quantity of milk in the new mixture is 56 liters.