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A vessel contains a mixture of milk and water in the respective ratio of 10 : 3. Twenty-six litre of this mixture was taken out and replaced with 8 litre of water. If the resultant respective ratio of milk and water in the mixture was 5 : 2, what was the initial quantity of mixture in the vessel ? (in litre)
Let quantity of Milk and water be M and W respectively.
M : W =10 : 3
3M=10W
In 26 litre of mixture
M =26(10/13) = 20 litre and
W =26(3/13) = 6 litre
8 litre of water is added.
Resulting ratio of M and W is
M-20 : W-6+8 = 5 : 2
2(M-20) = 5(W+2)
2M - 40 = 5W + 10
Multiplyin all the terms by 2.
4M - 80 = 10 W + 20
Replacing 10W with 3M.
4M - 80 = 3M + 20
M = 100
Hence W would be 30.
Total quantity = 100+30 = 130.
Option E is the correect answer.
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