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Management Aptitude Test 2017 Paper

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Question : 93 of 200

Marks: +1, -0

A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation, he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station, it is found that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container, if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?

7 gallons
14 gallons
21 gallons
28 gallons

Solution:

(d) 28 gallons

Let, the initial amount of liquid soap be 'x' gallons.

Ratio of the liquid soap left in the container to that of water =

\frac{36}{13}

∴ Amount of liquid soap left =

\frac{36x}{49}

Now, according to formula,

\frac{36x}{49} = x \left(1 - \frac{4}{x}\right)^2

⇒

\frac{6}{7} = \frac{x-4}{x}

⇒

\frac{6x}{7}

= x - 4

∴ x = 28 gallons.

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