Question

) two vessels contain mixtures of milk and water in the ratio of 8: 1 and 1: 5 respectively. The contents of both of these are mixed in a specific ratio into a third vessel. How much mixture must be drawn from the second vessel for fill the third vessel (capacity 26 gallons) completely in order that the resulting mixture may be half milk and half water?

Answer 1

Answer:

14 Gallons

Step-by-step explanation:

Let the mixture drawn from 1st vessel V1 = 9X gallons

and that from the 2nd vessel V2 = 6Y gallens.

Now as per the condition, 9X + 6Y = 26

The resulting mixture is half milk and half water, i.e. 13 gallons of milk and 13 gallons of water.

From 1st vessel, there is 8X gallons of milk and X gallons of water (ration 8:1)

From 2nd vessel, there is Y gallons of millk and 5Y gallons of water (ration 1:5)

∴ Total milk from both vessels will be

8X + Y = 13 ..... (1)

and total water from both vessels will be

X + 5Y = 13  .....(2)

Solving equation 1 and 2

Multiply en 1 by 5, we get

40X + 5Y = 65 ...(3)

Eqn 3 - Eqn 2  =

39X - 0 = 52

∴ X = 52/39 = 4/3

Substituting in eqn 2..

4/3 + 5Y = 13

∴ 4 + 15Y = 39

∴ 15Y = 35

∴ Y = 7/3

∴ Mixture from 2nd vessel = 6Y = 6 * 7/3

∴ Mixture from 2nd vessel = 14 gallons