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A and B can do a work in 10 days. B and C in 12 days, while C and A

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Bunuel
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A and B can do a work in 10 days. B and C in 12 days, while C and A [#permalink] New post   27 Apr 2021, 07:15
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A
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C
D
E

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35% (medium)

Question Stats:

72% (01:53) correct 28% (01:54) wrong based on 120 sessions
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A and B can do a work in 10 days. B and C in 12 days, while C and A in 15 days. How long would they take if all the three work together?

(A) 4 days
(B) 5 days
(C) 7 days
(D) 8 days
(E) 9 days
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D
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Re: A and B can do a work in 10 days. B and C in 12 days, while C and A [#permalink] New post   27 Apr 2021, 19:51
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Given: A and B can do a work in 10 days. B and C in 12 days, while C and A in 15 days.
Time taken by all of them together?

Let rate of A = a, rate of B = b, rate of C = c, Work done = w, time taken by all three of them = t.
We want the value of t in:
(a + b + c) * t = w

From data:

(a + b) * 10 = w
(b + c) * 12 = w
(a + c) * 15 = w

From above three equations:
(a + b) + (b + c) + (a + c) = \(\frac{w}{10}\) + \(\frac{w}{12}\) + \(\frac{w}{15}\) = \(\frac{w}{4}\)
=> 2 * (a + b + c) = \(\frac{w}{4}\)
=> (a + b + c) * 8 = w

=> t = 8 days.

So, correct answer is option D.
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Re: A and B can do a work in 10 days. B and C in 12 days, while C and A [#permalink] New post   15 Jul 2021, 10:04
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Bunuel wrote:
A and B can do a work in 10 days. B and C in 12 days, while C and A in 15 days. How long would they take if all the three work together?

(A) 4 days
(B) 5 days
(C) 7 days
(D) 8 days
(E) 9 days

Solution:

If we let a, b, and c be the number of days it takes A, B, and C to each complete the work alone, respectively, we can create the equation:

1/a+ 1/b = 1/10, 1/b + 1/c = 1/12, and 1/c + 1/a = 1/15

If we add the three equations, we have:

2/a + 2/b + 2/c = 1/10 + 1/12 + 1/15 = 1/4

1/a + 1/b + 1/c = 1/8

We see that their combined rate is 1/8 of the job per day; therefore, it takes them 1/(1/8) = 8 days to complete the work when the three are working together.

Answer: D
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Re: A and B can do a work in 10 days. B and C in 12 days, while C and A [#permalink] New post   27 Apr 2021, 22:52
Ans D 8 days.

Refer to the below diagram.
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Re: A and B can do a work in 10 days. B and C in 12 days, while C and A [#permalink] New post   19 Feb 2023, 11:26
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Re: A and B can do a work in 10 days. B and C in 12 days, while C and A [#permalink]
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