SSC CGL 16 Aug 2015 Shift 2 Paper

Question : 146 of 200

Marks: +1, -0

A and B together can do a piece of work in 30 days. B and C together can do it in 20 days. A starts the work and works on it for 5 days, then B takes up and works for 15 days. Finally C finishes the work in 18 days. The number of days in which C alone can do the work when doing it separately is :

120 days
24 days
60 days
40 days

Validate

Solution:

Let C complete the work in x days.
∴ B’s 1 day’s work =

1/{20}-1/x

and, A’s 1 day’s work
=

{2-3}/{60}+1/x

1/x-1/{60}

According to the question,
5

(1/x-1/{60})

+ 15

(1/{20}-1/x)

{18}/x

= 1
⇒

5/x

1/{12} + {15}/{2}

{1}/x + {18}/x

= 1
⇒

5/x - {15}/x + {18}/x

= 1 +

1/{12}-3/4

⇒

({5-15+18}/x)

{12+1-9}/{12}

⇒

8/x

1/3

⇒ x = 8 × 3 = 24 days

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