Equal quantities of three mixtures of milk and water are mixed in the ratio 1 : 2, 2 : 3

Ques - Equal quantities of three mixtures of milk and water are mixed in the ratio 1 : 2, 2 : 3 and 3 : 4. The ratio of water and milk in the mixture is ?

(a) 193 : 122

(b) 122 : 193

(c) 61 : 97

(d) 137 : 178

Solution - 

Given,

The ratio of three mixtures of milk and water = (1 : 2), (2 : 3), (3 : 4)

Total quantities of mixture A = 1 + 2

= 3

Total quantities of mixture B = 2 + 3

= 5

Total quantities of mixture C = 3 + 4

= 7

Now,

Equal quantities of three mixtures of milk and water are mixed.

Then,

Take the L.C.M of 3, 5, 7 = 105

Lets,

Assume each mixture contains 105 units.

Ratio of mixture A = 1 : 2

Milk in mixture A = (105/3) × 1

= 35

Water in mixture A = (105/3) × 2

= 70

Ratio of mixture B = 2 : 3

Milk in mixture B = (105/5) × 2

= 42

Water in mixture B = (105/5) × 3

= 63

Ratio of mixture C = 3 : 4

Milk in mixture C = (105/7) × 3

= 45

Water in mixture C = (105/7) × 4

= 60

Therefore,

Overall mixture of Water and Milk = (70 + 63 + 60) : (35 + 42 + 45)

= 193 : 122

Thus,

The ratio of water and milk in the mixture is 193 : 122.

Hence,

The correct answer is option (a) 193 : 122.

Thank You