Three bottles of equal capacity have mixture of milk and water in ratio 5 : 7, 7 : 9 and 2 : 1 respectively. These three bottles are emptied into a large bottle. What is the percentage of milk in the new mixture?

Three bottles of equal capacity have mixture of milk and water in ratio 5 : 7, 7 : 9 and 2 : 1 respectively. These three bottles are emptied into a large bottle. What is the percentage of milk in the new mixture?
1). 49.6
2). 52.3
3). 51.2
4). 50.7

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Guest · Answer 1 · 2019-07-17 17:12:31

Let the capacity of each bottle be y

For bottle 1, milk be 5a and water be 7a

⇒ 5a + 7a = y

⇒ a = y/12 …(i)

For bottle 2, milk be 7b and water be 9b

⇒ 7b + 9b = y

⇒ b = y/16 …(ii)

For bottle 3, milk be 2c and water be c

⇒ 2c + c = y

⇒ c = y/3 …(iii)

⇒ Percentage of milk can be given as = (5a + 7b + 2c) × 100/(5a + 7b + 2c + 7a + 9b + c)

⇒ Percentage of milk = (5a + 7b + 2c) × 100/(12a + 16b + 3c) …from (i), (ii) and (iii)

⇒ Percentage of milk = (5 × y/12 + 7 × y/16 + 2 × y/3) × 100/(y + y + y)

⇒ Percentage of milk = 50.7%

∴ the percentage of milk be 50.7%

Three bottles of equal capacity have mixture of milk and water in ratio 5 : 7, 7 : 9 and 2 : 1 respectively. These three bottles are emptied into a large bottle. What is the percentage of milk in the new mixture?

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