UPSC 2014 CDS II Math Paper

Let the work, W be completed in n days.
Work done by A in 2 days + Work done by B in n days + Work done by C in (n – 2) days = W
⇒

1

4

+

n

12

+

n−2

15

=1
⇒

15+5n+4n−8

60

=1
⇒9n+7=60
⇒n=

53

9

=5

8

9

days
Alternative Method:
(A + B)’s 2 day’s work
=2(

1

8

+

1

12

)=

10

24

=

5

12

∴ Remaining work=1−

5

12

=

7

12

(B + C)’s 1 day’s work
=

1

12

+

1

15

=

9

60

=

3

20

Required number of days
=5

8

9

days