# 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 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...

Why you convert 4/5 into 5/4?

NARAYAN SAHOO said:   1 decade ago
x=40-8=32 ratio 2 capacity 1
y=16 ratio 1 capacity 2

Together done ration 3
Work is 40
Then 40/3
13.1/3

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.

Can't get it because what does it mean of 16*5/4?

Ya we can't get. The remaining work of y is 4/5. But it taken has 5/4.

Heena roy said:   1 decade ago
X's 1 day work 1/40 ? how ?

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.

Keerthi said:   9 years ago
How to solve using LCM method?

Miftah said:   9 years ago
The main reason for 16*5/4 is unitary method. It goes like this:

It takes 4/5 work to completed by C = 16 days.

So for 1 work it will take: 16*5/4.