Aptitude - Time and Work - Discussion

Please explain the 3rd step.

Why 3 is multiplied by 5 in the last step? Please tell me.

A=30
B=20
C=60

Now take the lcm that is 60 mean A will make 3 chairs for example in one day B will make 2 chairs in one day and will make c will make 1 chair ( chairs example is for understanding).

Now A will make 3 chairs in one day and after 3 days it will make 9chair ( 3 *3) and at the third day ( B +c) will also make 3 chairs mean at the third day A +B +C WILL MAKE 12 chair in 3 days to make 60 chairs which our lcm it will require 15 days ( 12*5 = 60) that is 3*5 is 15 days.

@All.

A is 1st-day work 1/20.
A is 2nd-days work 1/2.
02/20.
a+b+c together work is = 1/20 + 1/30 + 1/60.

Add 2/20+1/20+1/30+1/60 = 1/5.
For 3 days = 1/5 * 1/3 = 1/15 ie 15 days.

How did (1/10+1/10) = 1/5 came?

Common multiple of A,B & C is 120.

A's one day work =120/20 = 6 units,
B's one day work =120/30 = 4 units,
C' one day work = 120/60 = 2 units,
work done in three days by A, B, C= 24 units.
So, the total work = (120/24) * 3 = 15 days.

LCM of A,B & C is 60.
so the total work to be complete is 60.
A->3units/day{60/20}.
B->2units/day{60/30}.
c->1unit/day(60/60}.
A's 2days work-> 3*2 = 6units.
3rd day A is assisted by B & C -> A + B + C.
A + B + C 1 day work->3 + 2 + 1 = 6.
2days A alone->6units.
3rd day->6 {A + B + C work}.
60/12 * 3 = 15.

A-20days
B-30days.
C-60days

LCM is 60
So,
A one day work 3 units (20*3)
B one day work 2 units(30*2)
C one day work 1 unit (1*60)

Then; 6 units ( both A+B+C one day work on every third day)
So A 2 days work = 3units *2 = 6 units
A+B+C on 3 Rd day = 6 units*1= 6 units
So, weget 12 units.

So 12/60 = 1/5 (A 2 days work +(A+B+C) work on a third day/total work)
So 3days * 1/5 = 15 days.
Here the answer.

Here in question, it is mentioned that A alone worked for 2 days, on the third day B and C assisted him.

So,
A's 2 days work= 2(1/20) = 1/10.
On third day three together worked.

i.e.,
3rd day work = (1/20)+(1/30)+(1/60) = 1/10.
Work done in 3 days= (1/10)+(1/10) = 1/5.
Total work is 3*5 = 15 days.

Take the LCM of A, B, C which is 60.

For LCM we have to multiply A, B, C by 3,2,1 respectively, this is work done per day by each of them.

For the first 2 days, only A works so, 2*3=6.
On the 3rd day A is assisted by B&C so,total work done in one day is 6units,
Therefore, the work they have done in 3days is 6+6=12,
Total work is done =60.
Days require to complete the work by A,B, C =60 ÷ 12=5days.
Days required by A to complete work = 5*3 = 15days.