Two containers of equal capacity are full of mixture of milk and water. In the first, the ratio of milk to water is 3 : 7 and in the second it is 7 : 9. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of milk to water?

Given:

Two containers of equal capacity with mixtures of milk and water.

First container ratio (Milk : Water) = 3 : 7

Second container ratio (Milk : Water) = 7 : 9

Formula used:

Let the capacity of each container be V .

Total milk in first container = \(\dfrac{3}{10}V\)

Total water in first container = \(\dfrac{7}{10}V\)

Total milk in second container = \(\dfrac{7}{16}V\)

Total water in second container = \(\dfrac{9}{16}V\)

Calculations:

Total milk = \(\dfrac{3}{10}V + \dfrac{7}{16}V\)

⇒ Total milk = \(\dfrac{48}{160}V + \dfrac{70}{160}V\)

⇒ Total milk = \(\dfrac{118}{160}V\)

⇒ Total milk = \(\dfrac{59}{80}V\)

Total water = \(\dfrac{7}{10}V + \dfrac{9}{16}V\)

⇒ Total water = \(\dfrac{112}{160}V + \dfrac{90}{160}V\)

⇒ Total water = \( \dfrac{202}{160}V\)

⇒ Total water = \(\dfrac{101}{80}V\)

Resulting ratio (Milk : Water) = \(\dfrac{59/80}{101/80}\)

⇒ Resulting ratio (Milk : Water) = 59 : 101

∴ The correct answer is option 1.