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 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?

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