Three containers have their volume in ratio 3:4:5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4:1), (3:1) and (5:2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is?
A. 4:1
B. 151:48
C. 157:53
D. 5:2
Ans: Let the ratio of milk and water in the first container be,
M1/W1=4/1
The ratio of milk and water in the second container be,
M2/W2=3/1
The ratio of milk and water in the third container be,
M3/W3=5/2
Since, the three containers are in the ratio 3:4:5,
In the first container,
M1+W1=3x---------(1)
M1/W1=4/1
=> M1=4W1-------------------(2)
Substituting (2) in (1),
4W1+W1=3x
=> 5W1=3x
=> W1=3x/5-----------(3)
Substituting (3) in (1) we get,
M1=12x/5
In the second container,
M2+W2=4x---------(4)
M2/W2=3/1
=> M2=3W2------------------(5)
Substituting (5) in (4) we get,
3W2+W2=4x
4W2=4x
W2=4x/4=x---------(6)
Substituting (6) in (4) we get,
M2=3x
In the third container,
M3+W3=5x---------(7)
M3/W3=5/2
=> 2M3=5W3
=> M3=5W3/2---------(8)
Substituting (8) in (7) we get,
5W3/2+W3=5x
=> 5W3 +2W3/7=5x
=> 7W3=10x
=> W3=10x/7----------(9)
Substituting (9) in (7),
M3=25x/7
Since all three mixtures are poured into the fourth container,
M4=M1+M2+M3 and
W4=W1+W2+W3
.: M4=12x/5 + 3x + 25x/7
=84x+105x+125x/35
=314x/35
.: W4=3x/5 + x +10x/5
=21x + 35x + 50x/35
=106x/35
M4/W4=314x/35÷106x/35
=157/53
=157:53(answer)
Good job
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