# 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 2 of 4.

Prashant singh said:   5 years ago
How 3/40 is converted to 40/3?

Ashis said:   6 years ago
Thanks for the solution @Mohit.

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)

Pooka said:   8 years ago
Thank you @Parthasarathy.

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

Gobind Mandal said:   8 years ago
Why did you convert 4/5 to 5/4?

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.

Chetan said:   8 years ago