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Bunuel
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One group of three of the four men can complete the work in 13 days wh 02 Dec 2020, 11:30
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A takes thrice as much time as B to complete a piece of work.
B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.

One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days and which is the group that takes 31 days?


A. 13 days group = (A, B, C); 31 days group = (A, B, D)

B. 13 days group = (A, B, D); 31 days group = (A, B, C)

C. 13 days group = (B, C, D); 31 days group = (A, B, C)

D. 13 days group = (A, C, D); 31 days group = (A, B, C)

E. 13 days group = (A, B, D); 31 days group = (A, B, D)


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One group of three of the four men can complete the work in 13 days wh 02 Dec 2020, 13:45
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Bunuel
A takes thrice as much time as B to complete a piece of work.
B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.
One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days and which is the group that takes 31 days?
A. 13 days group = (A, B, C); 31 days group = (A, B, D)
B. 13 days group = (A, B, D); 31 days group = (A, B, C)
C. 13 days group = (B, C, D); 31 days group = (A, B, C)
D. 13 days group = (A, C, D); 31 days group = (A, B, C)
E. 13 days group = (A, B, D); 31 days group = (A, B, D)
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A takes thrice as much time as B to complete the work. => Efficiency of A = 1/3rd of the efficiency of B
Assuming efficiency of A = 1 unit per day, we have:
Efficiency of B = 3 units per day
B takes thrice as much time as C to complete the work. => Efficiency of B = 1/3rd of the efficiency of C
Efficiency of C = 9 units per day
C takes thrice as much time as D to complete the work. => Efficiency of C = 1/3rd of the efficiency of D
Efficiency of D = 27 units per day

Note that a group of 3 of them take 13 days and another group of 3 take 31 days
Thus, ratio of efficiencies of these 2 groups = 31 : 13 respectively

We have the efficiencies: A = 1, B = 3, C = 9 and D = 27
Observe that A+B+C = 13 and A+B+D = 31 (efficiencies)
Thus, A, B and C take 31 days and A, B and D take 13 days

Answer B
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One group of three of the four men can complete the work in 13 days wh 03 Dec 2020, 03:05
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Hi seniors,

can anyone please explain this question using the common approach of w = r*t ? I am unable to comprehend the solution
provided above by Sujoy. Thank you a lot in advance!
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One group of three of the four men can complete the work in 13 days wh 04 Mar 2025, 00:15
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A takes thrice as much time as B to complete a piece of work.
B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.

One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days.

Which is the group that takes 13 days and which is the group that takes 31 days?

Let us assume that D takes x days to complete the work
C takes 3x days to complete the work
B takes 9x days to complete the work
A takes 27x days to complete the work

D is fastest and A is slowest.

Therefore, the group of (B,C,D) will take lowest time and the group of (A,B,C) will take highest time

Time taken by (B,C,D) to complete the work = 1/(1/9x + 1/3x + 1/x) = 9x/13
Time taken by (A,B,C) to complete the work = 1/(1/27x + 1/9x + 1/3x) = 27x/13
Time taken by (A,B,D) to complete the work = 1/(1/27x + 1/9x + 1/x) = 27x/31

If 27x/31 = 13; x = 13*31/27
27x/13 = 31

A. 13 days group = (A, B, C); 31 days group = (A, B, D)

B. 13 days group = (A, B, D); 31 days group = (A, B, C)

C. 13 days group = (B, C, D); 31 days group = (A, B, C)

D. 13 days group = (A, C, D); 31 days group = (A, B, C)

E. 13 days group = (A, B, D); 31 days group = (A, B, D)

IMO B
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One group of three of the four men can complete the work in 13 days wh 16 Mar 2025, 22:20
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Hey,

Can you please explain how are you getting an integer by equating the days worked by A, B and D to 13 days. Even if I go by trial and error, this option is not equal to 13

\(27(x)/31=13\)
\(x=(31*13)/27\)

x= 14.92 days which is not an integer

The logic for equating the option is not clear and even if you are trying to find an integer value of x, B does not match.

Thank you in advance:)

Kinshook
A takes thrice as much time as B to complete a piece of work.
B takes thrice as much time as C to complete the work.
C takes thrice as much time as D to complete the work.

One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days.

Which is the group that takes 13 days and which is the group that takes 31 days?

Let us assume that D takes x days to complete the work
C takes 3x days to complete the work
B takes 9x days to complete the work
A takes 27x days to complete the work

D is fastest and A is slowest.

Therefore, the group of (B,C,D) will take lowest time and the group of (A,B,C) will take highest time

Time taken by (B,C,D) to complete the work = 1/(1/9x + 1/3x + 1/x) = 9x/13
Time taken by (A,B,C) to complete the work = 1/(1/27x + 1/9x + 1/3x) = 27x/13
Time taken by (A,B,D) to complete the work = 1/(1/27x + 1/9x + 1/x) = 27x/31

If 27x/31 = 13; x = 13*31/27
27x/13 = 31

A. 13 days group = (A, B, C); 31 days group = (A, B, D)

B. 13 days group = (A, B, D); 31 days group = (A, B, C)

C. 13 days group = (B, C, D); 31 days group = (A, B, C)

D. 13 days group = (A, C, D); 31 days group = (A, B, C)

E. 13 days group = (A, B, D); 31 days group = (A, B, D)

IMO B
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