Aptitude - Time and Work - Discussion

How this 2 step comes 1/60? explain please.

day-1, day-2, day-3.
A. A. A+B+C.

Every 3rd-day b & c joining.

So 3(3A+B+C)=3(1/20)+1/30+1/60,
=9+2+1/60,
=1/5,
3A+B+C=1/3*5.
=1/15.
15 days work is complited.

LCM method:

The LCM of A,B,C is 60 so consider total work to be 60 unit.
Since A take 20 days, he does 3 unit per day.
Similarly, B does 2 unit per day.
Similarly, C does 1 unit per day.

So total unit of work done by 3 combined is 6 unit.

So by Addition of each day of Unit of work done until reaching total work. So the addition of A alone and A+B+C can be summarized as.
A doing work for first 2 days will be 2*3, total Work 6 done.
On 3rd day work done is 6, total work done 12.
Again A working alone for 4th and 5th is 2*3 =6,
Total work 18
On 6th day work done (A+B+C) 6, Total work 24
On 7th and 8th A is 6, total work 30.
On 9th day again (A+B+C) work done 6, TOTAL 36.
On 10 and 11th A alone work was done 6, Total work 42.
On 12th (A+B+C) work done 6, Total work 48.
On 13 and 24th A alone is 6, Total work 54.
On 15th A+B+C is 6, Total work was done 60 unit, work completed.

As A does work in 20 days.
B does in 30 days.
C does in 60 days.

Take the lcm and you will get total work = 60 parts.
No of parts A does work = 60/20 = 3 part / day.
Similarly B = 2 parts /day and c= 1 parts/day.
If A does work for 2 days he covers 3+3 parts = 6 parts.
And every third day B & C joins and then A + B +C = 6 parts on 3rd day.
Total work from first day to third day = 6 + 6 parts= 12 parts.
Total work = 60 parts.

Therefore no of days require = 5 * 3 = 15 days.

Why 3 is multiplied with 5 at last?

Please explain.

I really didn't get the last step where they said whole work will be done in 15 days. Can anyone explain how it comes?

A work in one day=1/20,
B work in one day=1/30,
C work in one day=1/60.

as A work for 2 days and then on third day B and C do work.
total work done in three days = A 3 days work+B 1 day work+ C one day work,
=3/20+1/30+1/60,
=9/60+2/60+1/60
=12/60.

Total work done in three days =1/5.
3=1/5part.

Let x days required to complete work=1 part.

3/x=1/5/1.
x=3*5=15 days.

@ALL. In simple method.

1/5 work is done in 3 days,
2/5 work is done in 6 days,
3/5 work is done in 9 days,
4/5 work is done in 12 days,
5/5 work is done in 15 days.

My answer is 17.
.
LCM = 60,
Efficiency of A = 3/day,
Efficiency of B = 2/day,
Efficiency of C = 1/day.
.
3+3+6+3+3+6+3+3+6+3+3+6+3+36+3+3= 60,

Total 17 days.

Thank you @Vikas, very good explanation.