Ratio analysis of work

WMDhamnekar

A can do a job 50% faster than B and 20% faster than C. Working altogether, they can finish the job in 4 days. How many days will it take A to finish the job if he works alone?

Answer:- I require some hint to answer this question. I am not able to form an equations showing the relation of variables in this question? As per my computation, A will require 10 days to finish the job if he works alone. But i don't know the correct answer. The author has not yet shown me a correct answer.

Last edited:

Cervesa

ratio of A's rate of work to that of B is 1.5 : 1
ratio of A's rate of work to that of C is 1.2 : 1

If $r$ is the work rate of A in jobs per day, then work rate of B is $\dfrac{r}{1.5}$ and work rate of C is $\dfrac{r}{1.2}$

working together,

$\left(r + \dfrac{r}{1.5} + \dfrac{r}{1.2}\right) \cdot (4 \text{ days}) = 1 \text{ job completed}$