Aptitude - Time and Work - Discussion

1 represents whole work..i.e
16X + 44Y =1
Means A having work for 16 days and B remaining in 44 so whole work is represented by 1 always.

Supplementary argument.
Like wise if A work 4/15 ( 16/60) and B remaining work 11 /15 ( 1- 4/15) which is done in 44 days.

4 / 15 + 11/15= 1 makes whole work.
Here we write X for A because we don't know As whole work alone and similarly Y for B too. The only thing we know is the remaining work.

Hope understand better now.

A+B do whole work in 30 days(100% of work or Complete).
A+B's1 day work =1/30.
Let us take assumption as usual.
A's 1 day work = x , & B's 1 day work = y.
=> x+y=1/30 ------------ eq1.
Now people got confused by;

This 16x +44y =1.
(Ans. It is equal to 1 coz 1 here means 100% or mathematically 1/1=1 and in eq1 1/30 means 1/30 100%work--1 divided into 30 parts has been done in 1 day 1/30%=3.3%).
And simply 1 means 100%. 1/1*%. Or 1/1x100.

Another way:

A + B = 60.
So A and B's together 1 day's work =1/60.

A's 1 day work = 1/16.
B's 1 day work = 1/44.

A works 16 days and leaves so int that A+B = 1/60, multiply A's work out of 60 days, Which gives number of work A has done.

Therefore 16/60=4/15 = A's work with B in 60 days.

Remaining work for 1 day = 1-4/15 = 11/15.

In those Remaining work has to Be done by B as he has to finish the work alone - 15/11*44 = 60 Days. This is Easy way.

A+B can do a work in 30 days.
One day work done by A =1/A.
One day work done by B=1/B.
1/A+1/B=1/30.

A worked for 16 days.
So one day work done by A =16/A.
Remaining work =1-16/A.
One day work done by B=1/B.
In 44day work done by B=44/B.
1-16/A=44/B.

16/A+44/B=1-----> eq1
1/A=1/30-1/B----> eq2

16(1/30-1/B)+44/B=1.
16/30+(44_16/B)=1,
16/30+28/B=1,
28/B=1-16/30,
28/B=30-16/30,
28/B=14/30,
28*30=14B,
B=840/14=60.

B shall finish whole work in 60 days.

Let total work = 1.

Work done by A is = x.

So remaining work that is done by B = 1-x.

So, total time to complete the whole work by A = 16/x....(1).

Similarly total time to complete the whole work by B = 44/(1-x).....(2).

From (1) and (2) we get.

16/x = 44/(1-x).....(3).

Solving (3) we get.

x = 4/15.

So 1-x = 11/15.

Now for B takes time 44 days to complete 11/15 work.

So total time to complete the whole work alone B = (15/11)x44 = 60 (ans).

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.

Don't consider x & y only consider x.
We know 16 days work of A + 44 days of B = total 1 work.
let work be x by both A & B.
now 16 days of x+44 days of x=1 work.
60 days x=1 work.
x=1/60.

Now find total work of B.
first find how much worked for 44 days ie-44*1/60=11/15.
now for 44 days he completed work of 11/15.
how many days he need to complete 1 work (total work) .
44*15/11=60 days.

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.

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.

I have figure out the easiest way to understand the equation:

Let's say the speed of work done by each A and B in one day:

A+B = 1/30 (that's mean only (1/30)*100 = 3.33% whole work done).

In order to complete the whole task is 100%.

So, 16A+44B = (100/100) = 1.

This explained why the number 1 exist in the equation. The other part can be solved on your own.