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1. Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take $\frac{8}{3}$ more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs. 450, then in how many days did A, B and C together complete the whole work?

A. 2 days

B. 4 days

C. 6 days

D. 8 days

Solution:

Ratio of efficiencies of A, B and C,
= 5x : 4x : 6x
Number of days required by A and B =

\frac{100}{9 x}

------ (1)
Number of days required by A, B and C =

\frac{100}{15 x}

------ (2)

\begin{aligned} \frac{100}{9 x} - \frac{100}{15 x} = \frac{8}{3} \\ \Rightarrow x = \frac{5}{3} \end{aligned}

Number of days required by A, B and C
=

\frac{100}{15 x}

\frac{100}{15 \times \frac{5}{3}}

= 4 days

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