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
Answer: b
Explanation: Ratio of efficiencies of A, B and C,
= 5x : 4x : 6x
Number of days required by A and B = $$\frac{{100}}{{9{\text{x}}}}$$ —— (1)
Number of days required by A, B and C = $$\frac{{100}}{{15{\text{x}}}}$$ —— (2)
$$\eqalign{
& \frac{{100}}{{9{\text{x}}}} – \frac{{100}}{{15{\text{x}}}} = \frac{8}{3} \cr
& \Rightarrow {\text{x}} = \frac{5}{3} \cr} $$
Number of days required by A, B and C
= $$\frac{{100}}{{15{\text{x}}}}$$
= $$\frac{{100}}{{15 \times \frac{5}{3}}}$$
= 4 days
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