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Adam, Brian and Charlie can complete a certain work in 75, 50 and 40

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Adam, Brian and Charlie can complete a certain work in 75, 50 and 40  [#permalink]

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New post 29 Feb 2020, 00:19
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Adam, Brian and Charlie can complete a certain work in 75, 50 and 40 days respectively. All 3 started working together, but Charlie took a leave in between and hence the work got completed in 18 days. For how many days was Charlie on leave?

A. 2
B. 3
C. 4
D. 5
E. 6
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Re: Adam, Brian and Charlie can complete a certain work in 75, 50 and 40  [#permalink]

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New post 29 Feb 2020, 01:21
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Dillesh4096 wrote:
Adam, Brian and Charlie can complete a certain work in 75, 50 and 40 days respectively. All 3 started working together, but Charlie took a leave in between and hence the work got completed in 18 days. For how many days was Charlie on leave?

A. 2
B. 3
C. 4
D. 5
E. 6


Let, Total Work = LCM (75, 50, 40) units = 600 units

i..e. A does 600 units in 75 days i.e.

A's work per day = 600/75 = 8 units
B's work per day = 600/50 = 12 units
C's work per day = 600/40 = 15 units

18days' work of A = 8*18 = 144 unit
18days' work of B = 12*18 = 216 unit

Work done by both A and B in 18 days = 144+216 = 360 units

Work Done by C = 600 - 360 = 240 units

C's days worked = 240 / 15 = 16 days


Charlie's leaves = 18 days - 16 days = 2 days

Answer: Option A
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Re: Adam, Brian and Charlie can complete a certain work in 75, 50 and 40  [#permalink]

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New post 29 Feb 2020, 01:57
let total work = 1;x
part of work completed by a&b in 18 days ;
18* ( x/75+x/50) ; 18*5x/150 ; 3x/5
so c would have completed ; 1-3x/5 ; 2x/5 of work
which it would completed in considering its rate in ;
2x/5 * 40 ; 16 days
so it means that c was on leave for 18-16; 2 days
IMO A


Dillesh4096 wrote:
Adam, Brian and Charlie can complete a certain work in 75, 50 and 40 days respectively. All 3 started working together, but Charlie took a leave in between and hence the work got completed in 18 days. For how many days was Charlie on leave?

A. 2
B. 3
C. 4
D. 5
E. 6
GMAT Club Bot
Re: Adam, Brian and Charlie can complete a certain work in 75, 50 and 40   [#permalink] 29 Feb 2020, 01:57
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Adam, Brian and Charlie can complete a certain work in 75, 50 and 40

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