Aptitude - Time and Work - Discussion

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

A:B = 1 : 1.

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

LCM Method

(A + B) 30 = 16A + 44B.
14A = 14B.
A/B = 1/1.

So one day work.
A = 1 unit.
B = 1 unit.
Total work = 30 x (1 + 1) = 60 units.
Time taken by B = 60/1 = 60 days.

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.

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.

@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.

90 days is the right answer.

A+B do 1 work in 30 days
A+B do 1/30 work in 1 day. --------> (1)

A+B do X work in 16 days
A+B do X/16 work in 1 day. --------> (2)

Eq 1 and eq 2 are eqaul, so.
1/30 = X/16
I.e. X= 8/15.

B alone work (1-X)work in (44-16)days.
Therefore, 1- 8/15 work in 28 days.

7/15 work in 28 days
1 work in 28 * 15/7 = 60 days,
Hence B finishes the whole work in 60 days.

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

60 days is the right answer!

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.