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A, B and C can all together do piece of work in 10 days, in which B takes three times as long as A and C together do the work and C takes twice as long as A and B together take to do the work. In how many days B can alone do the work?
  • a)
    35 days
  • b)
    33 days
  • c)
    43 days
  • d)
    40 days
  • e)
    45 days
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A, B and C can all together do piece of work in 10 days, in which B ta...
(A+C) in x days so B completes in 3x days
then (1/x) + (1/3x) = 1/10
solve, x = 40/3
so B in 3x = 3*(40/3)= 40 days
OR
Given A+B+C = 10 and that B takes 3 times as A+C, so A+C is three times stronger than B
So this means that 4 times stronger can do work in 10 days
So 1 time stronger(B) in 4*10 = 40 days
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Community Answer
A, B and C can all together do piece of work in 10 days, in which B ta...
Given:
A, B and C can do a piece of work together in 10 days.
B takes three times as long as A and C together do the work.
C takes twice as long as A and B together take to do the work.

Let's assume that A takes x days to do the work.
So, B will take 3(x + C) days to do the work as per the given condition.
And, C will take 2(x + B) days to do the work as per the given condition.

Now, let's find the individual efficiencies of A, B and C:
Efficiency of A = 1/x
Efficiency of B = 1/3(x + C)
Efficiency of C = 1/2(x + B)

Let's add the individual efficiencies to find the combined efficiency:
1/x + 1/3(x + C) + 1/2(x + B) = 1/10

Simplifying the equation:
6(x^2) + 23xC - 60B = 0

Now, we need to find the value of B. Let's substitute the value of C and simplify the equation:
C = 2(x + B)
6(x^2) + 23x(2x + 2B) - 60B = 0
12x^2 + 46xB - 60B = 0
6x^2 + 23xB - 30B = 0
x = 10B/3

Now, let's substitute the value of x in the equation 6(x^2) + 23xC - 60B = 0 and simplify it:
6[(10B/3)^2] + 23(2(10B/3) + B) - 60B = 0
200B^2 - 1080B = 0
B = 5.4 or 54/10

Therefore, B can alone do the work in 54/10 or 5.4 days (approx).
Hence, the correct answer is option D - 40 days.
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A, B and C can all together do piece of work in 10 days, in which B takes three times as long as A and C together do the work and C takes twice as long as A and B together take to do the work. In how many days B can alone do the work?a)35 daysb)33 daysc)43 daysd)40 dayse)45 daysCorrect answer is option 'D'. Can you explain this answer?
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