Aptitude - Time and Work - Discussion

Please help me to get this, why you take (1/20 * 4)?

Please help me to understand this, why we took 15/2 instead of 2/15?

Thank in advance.

Total work = X.

A = X (begin the work and he is in End of the work).

B = X-4 (After 4 days he joined).

= X/20 + X - 4/12 = 1.

= 3X + 5X - 20/60.

8X = 80.

X = 10.

They said in question in a piece of so how it's possible whole work done by them.

x can do a work in 20 days.

y can do a work in 12 days.

To find total work, take LCM of 20 and 12 i.e. 60.

So x+y total 1 day's work = (1/20+1/1/12) = 2/15.

But x work alone = 1/4 day's. Remain work = (1-1/4) = 3/4.

Now, work will be done by x and y = 2/15*3/4 = 1/10.

So 10 day's.

x+4/20+x/12 = 1.
3(x+4)+5(x)/60 = 1.
3x+12+5x = 60.
8x+12 = 60.
8x = 60-12.
8x = 48.
x = 6.
i.e., x+4 = 6+4.

10 days.

(4/20)+x(1/20+1/12) = 1,
Solve for x.
x=6.
Total days = x+4.

Can we do like this?

(4/20)+(x/12)=1.
It give 9.6 and dats means 10days.

X"s one day work is 1/20.
so he worked 4 days alone which is,
4* 1/20 = 1/5 remember the Confusion avoider formula below,
(Days * single day"s work( together or alone, this case alone by X) = completed work) remember this
when we know days RHS is Completed work, if Days not known RHS is Pending work
1/5 work is completed out entire work 1
entire work - completed work = 1-1/5 = 4/5 or 80% which is pending work
pending work is 4/5 which is done by X and Y
one day's work of X and Y is 1/20 + 1/12 = 2/15 this is 1 day"s work and Inverse is the Days. If you ask WHY see X 1/20 is one day's work of X, inverse which is 20 is the number of days. Is it clear?

15/2 * 4/5= 6 days
Use this formula.

Days * single day's work ( this case by X and Y) = remaining or completed work.
Days we have to find * 2/15 = 4/5 which gives 4/5* 15/2 =6.

Now 6 days for 80% or 4/5 of the job by x and Y and 4 days for initial 1/5 or 20% of the job by x.

So, total 10 days.

4/20+x/20+x/12=1.

X=6 so total days=6+4=10days.