# 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.

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)

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)

Mohit said:   8 years ago
First LCM of 40 is 40,

x can work 40 days,

work = 1 unit,

8*1 = 8,

remaining work 40 - 8 = 32,

Y finished it in 16 days then = 32/16 = 2,

x+y = 1+2 = 3,

(2)

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)

Yeezuu said:   4 years ago
(1)

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)

Atul said:   5 years ago
Wonderful explanation, thanks @Mohit.
(1)

P.muthukumar said:   8 years ago
What is the reason for converting 4/5 to 5/4?

Ria Sharma said:   3 years ago
Thank you @Mohit.

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.