Question

George can do some work in 8 hours paul can do some work in 10 hours while Hari can do the same work in 12 hours.All the three of them start working at 9AM.while George stops work at 11am the remaining two complete the work approximately when will the work be finished​

Answer 1

Answer:

george complete the work on 8pm.

Paul complete the work on 11pm.

hari complete the work on 12pm

Answer 2

Answer:

The work will be completed at 1 PM

Step-by-step explanation:

George can do work in 8 hours

So, George's 1 hour work $=\frac{1}{8}$

Paul can do work in 10 hours

So, Paul's 1 hour work $=\frac{1}{10}$

Hari can do work in 12 hours

So, Hari's 1 hour work $=\frac{1}{12}$

Total work is LCM of 8, 10, 12 $=120\hspace{0.1cm}parts$

George's 1 hour work $=\frac{120}{8}=15\hspace{0.1cm}parts$

Paul's 1 hour work $=\frac{120}{10}=12\hspace{0.1cm}parts$

Hari's 1 hour work $=\frac{120}{12}=10\hspace{0.1cm}parts$

(George + Paul + Hari)'s 1 hour work$=(\,15 + 12 + 10)\, =37\hspace{0.1cm}parts$

Given that all three started work at 9 AM and George stops work at 11 am and remaning two complete the rest of the work.

This means, all three worked for 2 hours.

(George + Paul + Hari)'s 2 hours work$=37 \times 2 =74\hspace{0.1cm}parts$

Work Remaining$=120 - 74 = 46\hspace{0.1cm}parts$

Now, we know Paul and Hari will work

(Paul + Hari)'s 1 hour work$=(\,12 + 10)\, =22\hspace{0.1cm}parts$

22 parts of work completed by (Paul +Hari) in 1 hour

46 parts of work completed by (Paul + Hari) in $\frac{46}{22}=2.1 \hspace{0.1cm}hours$

Thus, work completed in approximately $(\,2 + 2.1 = 4)\,$ hours as per the given scenario.

If work started at 9. AM, then work is completed at 1 PM