Aptitude - Time and Work - Discussion

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).

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.

@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.

A+B completes work in 30 days, so,

=>unit of work done by both A and B in 1 day = 1/30,
Consider that total work done by both A and B = 30 units,
So,in 1 day = 1 unit work is done,
Since 1 day = 1 unit of work then A do 16 units of work,
Remaining work = 30-16 = 14 units,
This 14 units of work is done by B in remaining 28 days(44 days-16 days).

If we see read the question we get that "the total number of days required by B to complete the total 30 units" is asked.
So we do like this,
for 28 days = 14 units,
x days = 30 units,
we get 14*x = 28 * 30,
=>x = 28*30/14,
=>x=60 days.

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.

Consider like this,

A and b completes a work in 30days. So this means both individually work for 30 days. Let us assume they do some bottles. If 60 bottles they have to do. It can be 30 bottles each or it can be 45 and 15 bottles or 40 & 20. So it depends upon each one capability.

So we can frame an equation like this,

30x+30y=1 (where x and why are the number of bottles per day. It is equated to 1 because for a day we are calculating).

Similarly, if A works for 16 days and B work for the 44 days,

So it will be 16x+44y = 1.

Solving and we will arrive at the answer.

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.

Let work done by A in 1 day be a and the work done by B in 1 day be;

A and B together can do a piece of work in 30 days.
=> Work done by A and B in 1 day = 1/30.
a + b = 1/30...........(1),

Work done by A in 16 days + work done by B in 44 days = 1.
16a + 44b = 1 ...........(2).

Solve (1) and (2)

Multiply equation (1) with 16 => 16a + 16b = 16/30=8/15 .......(3)
Subtract equation (3) from (2) => 28b = 1 - 8/15=7/15,
b = 7/15 * 1/28=1/60.

i.e., B alone needs 60 days to finish the work.

A and B complete work in 30 days.

A+B = 30.

A finished work in 16 Days and Remaining worked finished by B in 44 days.

It means 16 + Remaining days = 44 days.

16-44 = 28 days.

So B takes 28 days to finish the work alone.

But A and B together Finished work in 30 days.

16+14 = 30.

If they work together it takes 14 days to complete remaining work.

But B takes 28 days it means.

Both together takes 30 days so only B will take 60 days to complete the work.

Sorry my thinking is different.