Aptitude - Time and Work - Discussion

Hi all

Can any one explain clearly above 1, that hw the answer would be x=1/60 & y=1/60............

I think we cant get it from abve eqns that 16x +44y=1
x+y=1/30

Multiply x+y=1/30 by 16 and that gives 16x+16y=8/15

subtract 16x + 16y = 8/15
-
16x + 44y =1
----------------
28y = 7/15
hence, y=1/60
substitute y= 1/60 in x+y=1/30 and we get, x=1/60

A's 16 days work + B's 44 days work = 1
(A+B) 16 days work + B's 28 days work = 1
but (A+B) 1 days work= 1/30
hence, (A+B) 16 days work = 8/15
therefore,
8/15 + B's 28 days work = 1
B's 28 days work = 1- 8/15
= 7/15
B's 1 days work = 1/60

For completion of one work it took A, B for 30 days.

So let A's one day work is x & B's one day work is y.

From above we can write 1 work=30x+30y.

But in second case a worked for 16 days & B worked for 44days.

Therefore,

16x+44y=1 work.

By solving we can get y=1/60 work.

How to solve alternative working days problem in time and work?

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.

I don't think we should bother about 30 days' combined work. That piece of problem is, I think, meant to confuse us. Because he wishes to know B's individual capacity of doing what is left out by A's individual work.

Whatever A leaves behind, B finishes it.

Hence it is as simple as 16+44 = 60 days.

If 8/15 of the work is done by A in 16 days, then remaining 7/15 of the work is done by B in 44 days right....then why not cross multiply for 15/15 of the work.

I am getting a wrong answer doing this. Can anyone explain please.

7/15 work ----- 44 days.
15/15 work ----- k days.

k = 44*15/7 = 94.28.

This answer can still be solved by only having the basic formulas in mind.
Let A take x and B take y days to complete the whole work.

From question, we know,
1/x+1/y = 30 . By solving this we get,

xy = 30x+30y ... (1).

Now, work done by A in 1 day is 1/x. Therefore in 16 days = 16/x.
Remaining work = 1-(16/x).

This remaining work is done by B in 44 days.
And we have assumed that B takes y days to complete the job.

So for B.

WORK : Days
1 : y
1-(16/x) : 44

Solving this equation we get,
xy = 44x+16y ... (2).

Comparing (1) and (2),
30x+30y = 44x+16y.

Solve this and we get x=y.!
Put this in first equation , i.e.
1/y+1/y = 1/30.
2/y = 30.

Therefore, y = 60!
Hence 60 days.

Lengthy, but easy and precise :).

I think there is a mistake in the understanding.

"A having worked for 16 days, B finishes the remaining work alone in 44 days"

Look at this line.

- A worked for 16 days
- B finishes remaining work "ALONE" in 44 days.

So, it is never mentioned that A worked 16 days alone. I think it should be interpreted as - A worked with B for 16 days and then stopped. B did the remaining in 44 days.

Thus Solution is -

Let A's 1 day's work = x and B's 1 day's work = y

Then, x + y = 1/30 and 16*(x + y) + 44y = 1

Solving we get,

16 * (x + y) + 44y = 1.
or 16 * 1/30 + 44y = 1.
or 44y = 1 - 16/30.
or y = (14/30)/44.

Thus B finishes the work in (44 * 30)/14 = 94.285714.