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# The days taken to built a wall individually by each of A, B, C, D and

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Math Expert
Joined: 02 Sep 2009
Posts: 62508
The days taken to built a wall individually by each of A, B, C, D and  [#permalink]

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07 Jan 2020, 06:15
1
2
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Difficulty:

55% (hard)

Question Stats:

56% (02:17) correct 44% (02:42) wrong based on 18 sessions

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The days taken to built a wall individually by each of A, B, C, D and E is 20 days, 15 days, 12 days, 10 days and 6 days. They divide themselves into two teams such that the days taken by the two teams to finish the work are in the ratio 1.5 : 4.5. Find the team that finishes earlier.

A. A, B
B. C, D, E
C. B, C
D. A, D, E
E. B, E

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Re: The days taken to built a wall individually by each of A, B, C, D and  [#permalink]

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10 Jan 2020, 00:33
Bunuel wrote:
The days taken to built a wall individually by each of A, B, C, D and E is 20 days, 15 days, 12 days, 10 days and 6 days. They divide themselves into two teams such that the days taken by the two teams to finish the work are in the ratio 1.5 : 4.5. Find the team that finishes earlier.

A. A, B
B. C, D, E
C. B, C
D. A, D, E
E. B, E

Let the total work = LCM(20, 15, 12, 10, 6) = 60 units
So, Rate of each person is
$$R_A$$ = 60/20 = 3 units/day
$$R_B$$ = 60/15 = 4 units/day
$$R_C$$ = 60/12 = 5 units/day
$$R_D$$ = 60/10 = 6 units/day
$$R_E$$ = 60/6 = 10 units/day
--> Total work done per day if they all work together = 3 + 4 + 5 + 6 + 10 = 28

Ratio of time taken by two teams to finish = 1.5 : 4.5 = 1 : 3
--> Work done by the teams are in the ratio = 3 : 1
--> Work done by the team that finishes earlier = $$\frac{3}{4}$$*28 = 21 units/day

Work done per day by the following teams:
A. A, B = 3 + 4 = 7 --> No
B. C, D, E = 5 + 6 + 10 = 21 --> Yes
C. B, C = 4 + 5 = 9 --> No
D. A, D, E = 3 + 6 + 10 = 19 --> No
E. B, E = 4 + 10 = 14 --> No

IMO Option B
Re: The days taken to built a wall individually by each of A, B, C, D and   [#permalink] 10 Jan 2020, 00:33
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