Question

The ratio of milk and water in two vessels having the same capacity is 9 : 5 and 10 : 7 respectively. If the mixtures are poured into a third vessel then, what will be the new ratio of water and milk in the third vessel.
1. 182 : 183
2. 294 : 185
3. 183 : 293
4. 293 : 183

Answer 1

Correct Answer - Option 3 : 183 : 293

Given:

Ratio of milk and water in two vessels = 9 : 5 and 10 : 7

Concept used:

(x₁ + x₂)/(y₁ + y₂) = a/b

x₁, x2 = quantities of 1st type item

y1, y2 = quantities of 2nd type item

a, b = final ratio

Calculation:

Let milk and water in 1st vessel = 9x and 5x

⇒ Milk and water in 2nd vessel = 10y : 7y

According to the question,

9x + 5x = 10y + 7y       [∵ Both quantity are same]

14x = 17y

⇒ x/y = 17/14

Milk and water in 1st vessel = 9 × 17 and 5 × 17

⇒ 153L and 85L

Milk and water in 2nd vessel = 10 × 14 and 7 × 14

⇒ 140L and 98L

Total in milk and water in 3rd vessel = (153 + 140) and (85 + 98)

⇒ 293 and 183

⇒ Ratio of milk and water = 293 : 183

∴ The new ratio of water and milk in the third vessel is 183 : 293