UPSC 2014 CDS II Math Paper

Let the time taken by B to complete the work, W be n days.
∴ Time taken by A to complete the work, W = (n - 40) days
Work done by A in 1 day = 3 × Work done by B in 1 day
∴

W

n−40

=3×

w

n

⇒3n−120=n⇒n=60
Work done by A in 1 day + Work done by B in 1 day
=

W

60−40

+

W

60

=

W

20

+

W

60

=

4

60

W=

W

15

∴ Number of days taken by both of them to complete the work
=

W

( W 15 )

=15days
Trick:
Efficiency of A is 300% and Efficiency of B is 100%
100(x)=300(x−40)
⇒x=60days
100(60)=400d
d=15days