Three vessels whose capacities are in ratio 7 ∶ 6 ∶ 4 are completely filled with milk mixed with water. The ratio of milk to water in the mixture of those vessels are as 3 ∶ 2, 2 ∶ 1 and 3 ∶ 1 respectively. Find the percentage of water in the new mixture obtained when half of first, one-third of second and two third of the third vessel is taken out and mixed together?

Question

Three vessels whose capacities are in ratio 7 ∶ 6 ∶ 4 are completely filled with milk mixed with water. The ratio of milk to water in the mixture of those vessels are as 3 ∶ 2, 2 ∶ 1 and 3 ∶ 1 respectively. Find the percentage of water in the new mixture obtained when half of first, one-third of second and two third of the third vessel is taken out and mixed together?

14.90%
33.97%
33.47%
13.90%
None of these

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 3 : 33.47%

Given:

Capacities ratio of vessel are 7 ∶ 6 ∶ 4 respectively.

Ratio of milk and water in three vessel are as 3 ∶ 2, 2 ∶ 1 and 3 ∶ 1 respectively.

Mixture that taken out is half of first, one-third of second and two third of the third.

Concept:

Quantity of milk/water = × total quantity of mixture

Calculation:

Let the quantity of mixture in all the three vessels are 7x, 6x and 4x respectively.

Milk in first vessel = (ratio of milk/total ratio) × total quantity of vessel

⇒ (3/5) × 7x = 21x/5

Water in first vessel = (ratio of water/total ratio) × total quantity of vessel

⇒ (2/5) × 7x = 14x/5

Milk in 2nd vessel = (ratio of milk/total ratio) × total quantity of vessel

⇒ (2/3) × 6x = 4x

Water in 2nd vessel = (ratio of water/total ratio) × total quantity of vessel

⇒ (1/3) × 6x = 2x

Milk in 3rd vessel = (ratio of milk/total ratio) × total quantity of vessel

⇒ (3/4) × 4x = 3x

Water in 3rd vessel = (ratio of water/total ratio) × total quantity of vessel

⇒ (1/4) × 4x = x

Now taken out quantity half of first, one third of second and two third of the third and mixed together.

⇒ 7x × (1/2) + 6x × (1/3) + 4x × (2/3)

⇒ (7x/2) + 2x + (8x/3)

⇒ 49x/6

Quantity of new mixture = 49x/6

Now taken out quantity half of first, one third of second and two third of the third of water and mixed together.

⇒ (14x/5) (1/2) + (2x) (1/3) + (x) (2/3)

⇒ (7x/5) + (2x/3) + (2x/3)

⇒ 41x/15

Quantity of water in new mixture = 41x/15

Now to find the percentage of water in the new mixture

⇒ (Quantity of water in new mixture/Quantity of new mixture) × 100

⇒ × 100

⇒ (246/735) × 100

⇒ 33.47%

Hence the percentage of water in the new mixture is 33.47%.