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A, B and C invested capitals in the ratio of 4 : 6 : 9. At the end of the business term, they received the profit in the ratio of 2 : 3 : 5. Find the ratio of their time for which they contributed their capitals.

A) 1 : 1 : 9
B) 2 : 2 : 9
C) 10 : 10 : 9
D) 9 : 9 : 10

Correct Answer:




D) 9 : 9 : 10

Description for Correct answer:

Let the required ratio of time be \( \Large t_1 : t_2 : t_3 \)

Then using

Ratio of investments = ratio of proportions
\( \Large 4t_1 : 6t_2 : 9t_3 = 2 : 3 : 5\)

Taking two first terms of the ratio,

\( \Large \frac{4t_1}{6 t_2} = \frac{2}{3} = >\frac{t_1}{t_2} = \frac{1}{1} = \frac{9}{9} \)

= > \( \Large t_1 : t_2 = 9 : 9 \)

Taking last two terms of the ratio,

\( \Large \frac{6t_2}{9t_3} = \frac{3}{5} = \frac{t_2}{t_3} = \frac{9}{10} \)

= > \( \Large t_2 : t_3 = 9 : 10 \)

So \( \Large t_1 : t_2 : t_3 = 9 : 9 : 10 \)

Part of solved Partnership questions and answers : >> Aptitude >> Partnership

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