UPSC Civil Services 2016 Prelims General Studies Paper II

Let the work done by Ram and Shyam be R and S respectively.
Given, (R+S)′s4 days work =

60

100

of work
⇒ (R+S)′s1 day work =

60

100

×

1

4

of work =

15

100

of work
After Ram takes leave:
S's 8 days work =(1−

60

100

) of work =

40

100

of work
⇒ S's 1 day work

40

100

×

1

8

of work =

5

100

of work
So, Ram's 1 day work =(R+S)′s1 day work −S 's 1 day work
=(

15

100

−

5

100

) of work
=

1

10

of work ]
∴ Ram will take 10 days to complete the entire job alone.