Aptitude - Time and Work - Discussion

A having worked for 16 days
B finishes the remaining work alone in 44 days
so,
B finish the whole work alone is = A having worked+B finishes the remaining work alone
B alone = 16 days + 44 days
= 60 days

Selvi: its wrong... because, we dont know a & b's one day work.

Above solution is not properly explained.

Let me try to make it more clear (mathematically or logically).

1 day = 24 Hours.
A worked x hours in 1 day (24 hours).
B worked y hours in 1 day (24 hours).

So, x + y = 24 hours ----- Eq 1.

Now A's 16 days' work in hours = 16 * x = 16x.

And B's 44 days' work in hours = 44 * y = 44y.

16x + 44y = 30 days together worked of A + B in hours = 30 * 24 = 720 hours.

So 16x + 44y = 720 ----- Eq 2.

Now Eq 2 - 16 * Eq 1.

16x + 44y = 720.
16x + 16y = 384.
0 + 28y = 336.

Y = 336 / 28 = 12 hours in 1 day.

So x = 12 hours in 1 day.

If A doesn't work then to B has to work 24 hours in order to finish 1 day work which is equal to 2 days for B.

So for 30 days work, B has to work 60 days (answer = 60 days).

How you got 16x + 44y = 1, thy said 16 days alone a worked remainig work finished by b is 44 days then how can you frame the equation from this given data, I cant get please make me to understand.

How can we write 16x+44y=1. I cant understand.

Selvi. You are wrong absolutely.

Let A's 1 day's work = x and B's 1 day's work = y.
Both A's and B's 1 day work=1/30
i.e (A's 1 day + B's 1 day)=1/30
i.e x + y = 1/30........eq1
now,
A having worked for 16 days, B finishes the remaining work alone in 44 days
i.e work done by A in 16 days = 16x
Remaining work done B= 1 - 16x
but Remaining work is done by B in 44days i.e 44y
i.e. 44y=1-16x
i.e 16x+44y=1........eq2
solving eq1 & eq2,
we get,x = 1/60 and y = 1/60
B's 1 day's work = 1/60.
Hence, B alone shall finish the whole work in 60 days.

Kanna you are right.

Kanna your explaination was good.

A's 1 day work ,consider X
B's 1 day work ,consider Y
(A+B) 1 day work=(X+Y)=1/30
next condition:
A works for 16 days=16*X
B works for 44 days for remaining work to complete=44*Y
to complete whole work;16X+44Y=1
by solving both equations ,we get
X=1/60,Y=1/60
B can complete work in 60 days.