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Bunuel
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A is thrice as efficient as B and hence takes 12 days less to complete 07 Jan 2020, 06:14
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73% (02:17) correct 27% (02:44) wrong based on 229 sessions

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A is thrice as efficient as B and hence takes 12 days less to complete a work as compared to B. Find the number of days in which they can complete the work while working together?

A. 3
B. 4.5
C. 6
D. 6.5
E. 7.5
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B
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A is thrice as efficient as B and hence takes 12 days less to complete 07 Jan 2020, 06:37
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Bunuel
A is thrice as efficient as B and hence takes 12 days less to complete a work as compared to B. Find the number of days in which they can complete the work while working together?

A. 3
B. 4.5
C. 6
D. 6.5
E. 7.5
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Set the rates as A and B. A = 3B, it takes A: \(\frac{1}{A }= \frac{1}{{3B}}\) days to complete the job and B: \(\frac{1}{B}\) days to complete the job.

The difference is 12 days, so \(\frac{1}{B} - \frac{1}{{3B}} = \frac{2}{{3B}} = 12\).

B = 2/(3*12) = 1/18, A = 3*B = 1/6.

Finally, their combined rate is A + B = 1/6 + 1/18 = 4/18 = 2/9, it will take 9/2 days to complete the job.

Ans: B
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A is thrice as efficient as B and hence takes 12 days less to complete 20 Dec 2021, 10:44
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Bunuel
A is thrice as efficient as B and hence takes 12 days less to complete a work as compared to B. Find the number of days in which they can complete the work while working together?

A. 3
B. 4.5
C. 6
D. 6.5
E. 7.5
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Let efficiency of B be e ; efficiency of a will be 3e

So, \(de = (d - 12)3e\)

Or, \(d = (d - 12)3\)

Or, \(d = 3d - 36\)

So, 2d = 36

hence, d = 18

Thus, time taken by both of them will be 18*1/3+1 = 4.5 days, Answer will be (B)
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A is thrice as efficient as B and hence takes 12 days less to complete 30 Dec 2021, 01:09
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Bunuel
A is thrice as efficient as B and hence takes 12 days less to complete a work as compared to B. Find the number of days in which they can complete the work while working together?

A. 3
B. 4.5
C. 6
D. 6.5
E. 7.5

Set the rates as A and B. A = 3B, it takes A: \(\frac{1}{A }= \frac{1}{{3B}}\) days to complete the job and B: \(\frac{1}{B}\) days to complete the job.

The difference is 12 days, so \(\frac{1}{B} - \frac{1}{{3B}} = \frac{2}{{3B}} = 12\).

B = 2/(3*12) = 1/18, A = 3*B = 1/6.

Finally, their combined rate is A + B = 1/6 + 1/18 = 4/18 = 2/9, it will take 9/2 days to complete the job.

Ans: B
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I am curious why "A is thrice as efficient as B" means A = 3B. eg, if it takes B 5 days to complete the job, so would it take A to complete 15 days? this should be thrice less as efficient as B from my understanding. I first go with 1/A = 3/B and it goes wrong. Please enlighten me.
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A is thrice as efficient as B and hence takes 12 days less to complete 19 Mar 2025, 10:23
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