Question

Two vessels contain mixtures of honey 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 to fill the third vessel (capacity 36 gallons) completely in order that the resulting mixture may be half honey and half water?

Answer 1

Let first vesselcontains 9x gallons of mixture and 2nd vessel contains 6y gallons of mixture.

in first vessel,

honey = 8x gallons , water = x gallons

in 2nd vessel,

honey = y gallons , water = 5y gallons

if contents of both of these are mixed in a 3rd vessels.

honey = 8x + y , water = x + 5y

a/c to question,

capacity of 3rd gallons is 36 gallons and resulting mixture contains half honey and half water.

so, honey = 8x + y = 36/2 = 18 gallons .....(1)

water = x + 5y = 36/2 = 18 gallons ......(2)

from equations (1) and (2),

39x = 90 - 18 = 72 ⇒x = 24/13

y = (18 - 24/13)/5= 42/13

now, mixture from 2nd vessel = 6y = 6 × 42/13 = 19.38 gallons.