P,Q and R can complete a job in 20 days, 30 and 40 days respectiely. They started working on it. Q and R left afte working for certain number of days and P alone completed the remaing work 7 days. Find the time taken to complete the job (in days)

Explanation

Let the time taken to complete the job be t days.
Job `=(t-7)` days of work of P,Q and R+7 days of work of P
`(t-7)((1)/(20)-(1)/(30)+(1)/(40)) ((1)/(20))`
`(t-7)((13)/20)+(7)/(20)=1rArr((t-7)(13)+42)/(120)=1`
`13(t-7)=78rArr t=13`