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Bunuel
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A and B can finish a work in 10 days when working together. B and C wo 07 Jan 2020, 07:12
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

73% (01:58) correct 27% (02:46) wrong based on 179 sessions

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A and B can finish a work in 10 days when working together. B and C working together can finish the same work in 12 days and A and C working together can finish the work in 15 days. In how many days will the work get over if all three A, B and C work together?

A. 5
B. 6
C. 8
D. 4
E. 3
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C
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A and B can finish a work in 10 days when working together. B and C wo 14 Jan 2020, 10:27
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Bunuel
A and B can finish a work in 10 days when working together. B and C working together can finish the same work in 12 days and A and C working together can finish the work in 15 days. In how many days will the work get over if all three A, B and C work together?

A. 5
B. 6
C. 8
D. 4
E. 3
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Let the total work be 60 Units (LCM of 10 , 12 & 15)

Thus, we have -

Efficiency of A + B = 6
Efficiency of B + C = 5
Efficiency of A + C = 4

Combined efficiency of \(A + B +C = \frac{6 + 5 + 4}{2} = \frac{15}{2}\)

Thus, Time required by A , B and C to complete the work is \(60*\frac{2}{15}=8\) , Answer must be (B)
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A and B can finish a work in 10 days when working together. B and C wo 15 Jan 2020, 16:56
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Where is the division of 2 coming from?
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A and B can finish a work in 10 days when working together. B and C wo 15 Jan 2020, 17:25
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2*( 1/a + 1/b + 1/c ) = 1/10 + 1/12 + 1/15
===>>> 1/a + 1/b + 1/c = 1/8

8 days

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A and B can finish a work in 10 days when working together. B and C wo 16 Jan 2020, 07:28
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Bunuel
A and B can finish a work in 10 days when working together. B and C working together can finish the same work in 12 days and A and C working together can finish the work in 15 days. In how many days will the work get over if all three A, B and C work together?

A. 5
B. 6
C. 8
D. 4
E. 3
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We can create the equations:

1/A + 1/B = 1/10

1/B + 1/C = 1/12

1/A + 1/C = 1/15

Adding the equations together, we have:

2/A + 2/B + 2/C = 1/10 + 1/12 + 1/15

2/A + 2/B + 2/C = 6/60 + 5/60 + 4/60

2/A + 2/B + 2/C = 15/60

2/A + 2/B + 2/C = 1/4

To determine 1/A + 1/B + 1/C, we multiply the above equation by ½, and we have:

1/A + 1/B + 1/C = 1/8

Therefore, the job can be completed in 1/(1/8) = 8 days if all 3 people work together.

Answer: C
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A and B can finish a work in 10 days when working together. B and C wo 07 Sep 2024, 01:26
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Let's assume following variables/values

    ◉ Rate of A = A
    ◉ Rate of B = B
    ◉ Rate of C = C
    ◉ Work Done = 1 (As Work done by everyone is same)

Formula to be used Rate * Time = Work

A and B can complete a work in 10 days

=> Combined rate of A and B = A + B
=> Rate * Time = Work
=> (A + B) * 10 = 1
=> A + B = 1/10 ...(1)

B and C can complete the same work in 12 days

=> Combined rate of B and C = B + C
=> Rate * Time = Work
=> (B + C) * 12 = 1
=> B + C = 1/12 ...(2)

A and C can complete that work in 15 days

=> Combined rate of A and C = A + C
=> Rate * Time = Work
=> (A + C) * 15 = 1
=> A + C = 1/15 ...(3)

If A, B and C are working together, how many days does it take to complete the work?

=> Combined rate of A, B and C = A + B + C
=> Rate * Time = Work
=> (A + B + C) * Time = 1
=> Time = 1 / (A + B + C)

(1) + (2) + (3)
=> A + B + B + C + A + C = 1/10 + 1/12 + 1/15
=> 2 * (A + B + C) = 6/60 + 5/60 + 4/60 = 15/60 = 1/4
=> A + B + C = 1/(2*4) = 1/8

=> Time = 1/(A + B + C) = 1 / (1/8) = 8

So, Answer will be C
Hope it helps!

Watch following video to MASTER Work Rate Problems

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