Question

What is the quantity of milk in 80 litres of the mixture of milk and water?
I. If 8 litres of the mixture is replaced by an equal quantity of water, the ratio of milk and water in the mixture becomes 27: 13 respectively.
II. If 16 litres of the mixture is replaced by an equal quantity of milk, the ratio of milk and water in the mixture 4: 1 respectively.

• A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
• B. If the data in the statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
• C. If the data either in statement I alone or in statement II alone is sufficient to answer the question.
• D. If the data in both the statements I and II together are not sufficient to answer the question.
• E. If the data in both the statements I and II together are necessary to answer the question.

Answer 1

The correct option is C If the data either in statement I alone or in statement II alone is sufficient to answer the question.

By statement - I
M : W = 27 : 13.
So, 80 litres of mixture contains
Quantity of milk $=\frac{27}{40}\times 80=54litres$
By statement - II,
If 16 litres of mixture is replaced by an equal quantity of milk, then in the new mixture,
Quantity of milk $=\frac{4}{5}\times 80$ = 64 litres.
Quantity of water $=\frac{1}{5}\times 80$ = 16 liters.
Again by the Statement -I,
Before mixing water, milk is 64 litres and water is 16 litres.
Statement - II: Before mixing milk 48 litres and water is 16 litres.
The ratio of milk to water in the mixture. = 3 : 1
Quantity of milk $=\frac{3}{4}\times 80=60litres$
Concept -> Ratio of milk to water is always same in the mixture. It doesn't depend on the quantity of mixture drawn.