Aptitude - Time and Work - Discussion

Then, In how many days shall B finish the whole work alone?

Anyone, please answer this.

Let's take A to complete a work in x days and B to complete a work in Y days.
A's 1 day work =1/x and B's 1 day work =1/Y.
A and B together complete a work in 30 days so 1/X +1/Y = 1/30.
A's 16 days of work = 16/X
Remaining work = 1-16/X = X-16/X.

B completes the remaining work in 44 days so X-16/X work will be completed by B in 44 days
B will complete the whole work in 44X/X-16 days which would be equal to Y (because B completed a work in Y days)
So, Y = 44X/X-16.
since 1/X+1/Y = 1/30.
so, 1/X+X-16/44X = 1/30,
44+X-16/44X = 1/30,
X+28/44X = 1/30,
30X+840 = 44X,
14X = 840,
X = 60 days.

60 days is the right answer!

90 days is the right answer.

A+B's 1days work = 1/30
A+B's 16days work = 1/30*16=8/15
Now,
B's 1day work =8/15-1/30=1/2
So, B's 16day work will be=1/2*16=8.

*Now we have to find out the remaining work*

Remaining work =(1-8/15)=7/15.
ATQ,

B does the remaining work,e.i 7/15 portion work in =44 days.
And 8 portions work in 16 days.

Therefore B shall finish the whole work alone in =(44days + 16days) = 60 days.

30A + 30B = 16A + 44B.

A:B = 1 : 1.

Capability of both are equal,
A+B = 30,
2person need = 30days.
1person need = 2 * 30 = 60days.

A worked 16 days.

If 16 days= x portion.
The remaining work is 1-x portion.
which portion B finished by 44 days.
Then,
1-x = 44,
1-16 = 44 (x=16),
1 = 44 + 16,
1 = 60 (1= total portion)
Am I right? Please tell me.

@All.

Here, You take total work is 30 units.

i.e A and B together if they work ,they can finish 1 unit per day ( as they can finish the total work in 30 days).

Now A worked for 16 days.

And, B worked for 44 days i.e we can say 44 days work means (16+28) days work.
Now you take only A's 16 days work and B's 16 days work i.e. (A+B)'s 16 days work= 16 units finish.
Remaining work = 30-16=14 units.
B's 16 days work is over .
i.e. B ' s remaining 28 days work is left which is equals to 14 units.
14 units in 28 days ( done by B).
B can do 0.5 units per day.
Total work 30 units.
So, B can do 30 units i.e. total work in 60 days.

Let total work = 30 units (As days are 30).

A+B = 30/30 i.e, they both do "1" unit of work.
If A works for 16 days i.e, he made "8" units only.
And B was left with 22 (30-8).
So, 22--> 44.
1--> 2.
ATQ, B's whole work alone:
30(total) * 2 = 60DAYS answer.

Average work = 60.
A = 16/60 = 4/15.
B=11/15*1/44=60.