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Two vessels contain a mixture of milk and water. In the first vessel, the ratio of milk and water is 5 : 2 and in the second vessel, the ratio is 8 : 5. A 54 L vessel is filled from these vessels so as to contain a mixture of milk and water in the ratio of 9 : 4. How many litres are taken from the first vessel?

Two vessels contain a mixture of milk and water. In the first vessel, the ratio of milk and water is 5 : 2 and in the second vessel, the ratio is 8 : 5. A 54 L vessel is filled from these vessels so as to contain a mixture of milk and water in the ratio of 9 : 4. How many litres are taken from the first vessel? Correct Answer 42 l

Given:

Two vessels contain a mixture of milk and water. In the first vessel; The ratio of milk and water 5 : 2 and in the second vessel the ratio is 8 : 5

Calculations:

Let 7x (5 + 2) quantity of 1st vessel is mixed with 13y ( 8 + 5) quantity of 2nd vessel.

Total milk in the final mixture = 5x + 8y

Total water in the final mixture = 2x + 5y

According to the question:

(5x + 8y)/(2x + 5y) = 9/4

20x + 32y = 18x + 45y

2x = 13y

x : y = 13 : 2

Quantity from 1st vessel :  Quantity from 2nd vessel = 91 : 26 = 7 : 2

Total volume of vessel = 54

From 1st vessel = 7 × 54/(7 + 2) = 7 × 6 = 42

 

 

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