Question

3 glasses A, B and C whose capacities are in the ratio
1:2:3 are filled with mixture of acid and water. The ratios of acid to water in A, B and C are 1:5, 3:5 and 5:7 respectively. The contents of these glasses are emptied into a single vessel. What is the ratio of acid to water in the vessel?

Answer 1

A:B:C = 1:2:3 = 12x : 24x : 36x

for A:
acid:water = 1:5 = (1/6)12x : (5/6)12x = 2x : 10x
for B:
acid:water = 3:5 = (3/8)24x : (5/8)24x = 9x : 15x
for C:
acid:water = 5:7 = (5/12)36x : (7/12)36x = 15x : 21x

now pouring this into one container in 1:2:3
from A we are getting 2x acid and 10x water
from B we are getting
9x acid and 15x water
from C we are getting 15x acid and 21x water

acid : water = (2x+9x+15x) : (10x+15x+21x)
= 26x : 46x
= 13 : 23

could have used a specific volume, e.g.
suppose A has 1200 ml, B has 2400 ml , C has 3600 ml, notice ratio of 1:2:3
in A we have 200 ml acid and 1000 ml water, 200:1000 = 1:5
in B we have 900 ml acid and 1500 ml water, 900:1500 = 3:5
in C we have 1500 acid and 2100 water, 1500:2100 = 5:7
total acid = 200+900+1500 = 2600
total water = 1000+1500+2100 = 4600
ratio of acid:water = 2600:4600 = 13:23