Aptitude - Time and Work - Discussion

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.

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+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.

90 days is the right answer.

60 days is the right answer!

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.

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

Anyone, please answer this.