Aptitude - Time and Work - Discussion

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.

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?

Why 3 is multiplied with 5 at last?

Please explain.

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.

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.

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.

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

Take LCM ot 20,30 and 60 you will get total units of work i.e 360 units.
Now find the 1 day work by using UNITS/DAYS.
A=18 units
B=12 units
C=6 units
Now A+B+C 1 day work is 18+12+6=36 units.
A+B+C will complete the work in 10 days(360/36).

Now, B and C joins every 3rd day which means A will work for 2 days alone and A+B+C will work on the 3rd day.

A 1day work = 18,
A 2 day work= 18*2=36 units,
A+B+C 1 day work is 36 units,
So 3 days of work =36+36= 72 units,
So 1-day work will be 72/3.

Now total work was 360 units.
Total days= 360*3/72 = 15 Days.

Simply;

A's 3 days works ----- 3/20.
B and C join on 3rd day so;
(A+B+C)'s 3 days work will be ---- 3/20 +1/30+ 1/60 = 12/60 = 1/5.
3 days work -- 1/5 then;
1 day work -- 1/15 part of 1 work (i.e 1/15 work in 1 days),
15 days = 1 work.

Nice explanation, Thanks.