Aptitude - Time and Work - Discussion

B finishes the remaining work in 44 days.
A finishes the work in 16 days,
So, B alone, 44 + 16 = 60 days.

x + y = 1/30 -----> (i)
16x + 44y = 1 ------> (ii)

Cross Multiply 30 in equation (i).

Now 30x + 30y = 1.
Now equate equation (i) and (ii) , since both equations are equal to 1,
We can write;

30x + 30y = 16x + 44y.
30x - 16x = 44y - 30y.
14x = 14y.
x = y.

Since x = y, apply to any one of the equation, let me put to equation (i)

Now, x+x = 1/30,
2x = 1/30,
x = 1/60,
Since x = y,
y = 1/60.

A work is x. ie. x work completed in 16 days.
B work is 1-x. ie. Remaining 1-x work completed in 44 days.
We need whole work completed ie. 1.
So,
A work + B work=1.
Therefore;

16+44 = 60days.

A worked 16 days.
A+B worked 30 days.
A+B = 1/30.

16 days A work = 1/30x16 = 8/15 remaining work 7/15. done by B.
B alone work 44-16 = 28.

So Alone B work done =28 x 15/7 = 60.

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.

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.

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.

Selvi. You are wrong absolutely.

A+B takes 30 days to complete whole work.
Their 1-day work
A=1/2 unit/day.
B=1/2 unit/day.
That means the total work of 30 days.
B alone will take 60 days.

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