# Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 28)
28.
X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

 13 1 days 3

15 days
20 days
26 days
Explanation:

 Work done by X in 8 days = 1 x 8 = 1 . 40 5

 Remaining work = 1 - 1 = 4 . 5 5

 Now, 4 work is done by Y in 16 days. 5

 Whole work will be done by Y in 16 x 5 = 20 days. 4

 X's 1 day's work = 1 , Y's 1 day's work = 1 . 40 20

 (X + Y)'s 1 day's work = 1 + 1 = 3 . 40 20 40

 Hence, X and Y will together complete the work in 40 = 13 1 days. 3 3

Discussion:
31 comments Page 1 of 4.

x's speed of work is 40, so work in 1 day is 1/40.

x does 8 days and leaves, so work done is 8*(1/40) = 1/5.

x does only 1/5 of the work , so remaining work to be done is 4/5 (1-1/5 = 4/5).

y's speed of work is not given, let us take it as 'K'. but he completes the remaining 4/5 work in 16 days.

So 16*(1/K)=4/5 which gives K = 20.

Now both together takes ( x speed of work + y speed of work).

1/40 + 1/20 = 3/40 = 1/(40/3) = 1/(13 1/3).

So the ans is 13 1/3.

Anonymous said:   3 years ago
@All.

For those who are asking why 5/4 is multiplied,

Let's take an example, Suppose You complete work 1/2 of a work in 2 days. In how much time will you complete the entire work. 4 days right, how did you get it? you multiplied 2.

Eg:

1/2 : 2 is as 1: x, (I took 1 as it is the complete work).

Solving that, you still will get 4 as the answer. Same logic you can apply.
Thank you.
(1)

Manu said:   7 years ago
The total work has done in two parts.
Y completed only 4/5 part of work. another part is done by X.
So work done by Y one day is 1/total work
= 5/4.

But, no need to get confused. simply solve as;
Y completed 4/5 part of work in 16 days.
one day's work is work/days.
divide 4/5 by 16.

We get the answer 1/20 directly.
(2)

Biswajit das said:   4 years ago
x in 40 days =100% work done.
Then in 08 days= 20 % work done.

The remaining work is 80 % which is done by Y in 16 Days.
in 16 Days =80 % work done.
Then in 20 Days =100 work done.
x=40.
y=20.

LCM =40 (Total work).
X one day work is 01 and 02 is Y's.
Then work done both x and y in= 40/3=13+1/3 Days.
(6)

Chetan said:   9 years ago

In other problems where same fractions were calculated, there we were finding remaining work. Here for Y, we are finding the Whole work. This could be the reason though I am not sure.

Mir Adil said:   5 years ago
If x does a work at 8 days out of 40 days remaining 32 days are left.

Then y does remaining 32 days work in 16 days itself so Their ratio is 1:2 totally they can do 3 parts in one day, So 3+3+3+3+3+3+3+3+3+3+3+3+3 it completes 39 days here and 1/2 to complete 40 days.
(1)

Makvana Disha said:   8 years ago
We are also do this,

x = 40days = 100%
For 8 days = ? (20%) so, 80% works remaining. That is done by y in 16 days.
80% = 16days
100% = ? (20days)

(x + y)'s 1 day work = (1/40) + (1/20).
= (3/40).
= (40/3) = 13*1/3.

x can do work=1/40--->1

Let 8x+16y=1---->2(which is x &y can do work)

sub x value in above equ. we get
8(1/40)+16y=1
y=1/20.
finally, x=y will together=(1/40)+(1/20)=3/40
Hence, ans is (40/3)=13 1/3 days...

Thiru said:   3 years ago
Take X's work as 1/40 he can do the work in only 8 days so 1/40*8=1/5.
Now 4/5 part of the work is remaining so Y is completing 4/5 part in 16 days 4/5 * 16 = 1/20.
Asking whole men's work1/20+1/40 = 13 1/3 days.

Let x can do 1 work in a hour. Then he will do 8 work in 8 hour.

Remaining work = 40-8 = 32.

32/y=16;
y=2.

Means y do 1 work in 2hours.
x+y=3.

Together they will do in 40/3 day.