In a partnership, A invests 16 th of the capital for 16 th of the time, B invests 13 rd of the capital for 13 rd of the time and C invests the rest of the capital for the whole time. Out of a profit of 4140, A’s share is:

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705-805

Fractions/Ratios/Decimals

In a partnership, A invests $\frac{1}{6}$ th of the capital for $\frac{1}{6}$ th of the time, B invests $\frac{1}{3}$ rd of the capital for $\frac{1}{3}$ rd of the time and C invests the rest of the capital for the whole time. Out of a profit of $4140, A’s share is:

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$100

$120

$180

Correct

$300

$540

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Explanation

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Official Explanation

Official

Let total capital = C, total time = T.

A invests

\frac{1}{6}C

for

\frac{1}{6}T

.

B invests

\frac{1}{3}C

for

\frac{1}{3}T

.

C invests the rest:

C - \left(\frac{1}{6}C + \frac{1}{3}C\right) = C - \frac{1}{2}C = \frac{1}{2}C

for the whole time T.

Profit sharing ratio is proportional to (investment × time):

A's share:

\left(\frac{1}{6}C\right) \times \left(\frac{1}{6}T\right) = \frac{1}{36}CT

B's share:

\left(\frac{1}{3}C\right) \times \left(\frac{1}{3}T\right) = \frac{1}{9}CT

…

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What this question tests

What it tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Common trap

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.

In a partnership, A invests 16\frac{1}{6}61​ th of the capital for 16\frac{1}{6}61​ th of the time, B invests 13\frac{1}{3}31​ rd of the capital for 13\frac{1}{3}31​ rd of the time and C invests the rest of the capital for the whole time. Out of a profit of $4140, A’s share is: