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A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
- a)8 hours
- b)10 hours
- c)12 hours
- d)24 hours
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A can do a piece of work in 4 hours; B and C together can do it in 3 h...
A's 1 hour's work = 1/4;
(B + C)'s 1 hour's work = 1/3;
(A + C)'s 1 hour's work = 1/2.
(A + B + C)'s 1 hour's work = (1/4 + 1/3) = 7/12.
B's 1 hour's work = (7/12 - 1/2) = 1/12.
Therefore,
B alone will take 12 hours to do the work.
Most Upvoted Answer
A can do a piece of work in 4 hours; B and C together can do it in 3 h...
Given Data:
- A can do the work in 4 hours
- B and C together can do the work in 3 hours
- A and C together can do the work in 2 hours
Work Rates:
Let the work rate of A be \(x\), work rate of B be \(y\), and work rate of C be \(z\).
Calculating Work Rates:
- Since A can do the work in 4 hours, A's work rate is \(\frac{1}{4} = \frac{x}{1}\) which implies \(x = \frac{1}{4}\).
- From the given data, we know that B and C together can do the work in 3 hours. Their combined work rate is \(\frac{1}{3} = \frac{y+z}{1}\).
- Similarly, A and C together can do the work in 2 hours. Their combined work rate is \(\frac{1}{2} = \frac{x+z}{1}\).
Solving the Equations:
Substitute the values of \(x\) and \(y\) into the equations above to find the value of \(z\).
\(\frac{1}{3} = \frac{\frac{1}{4}+z}{1}\) (Substitute \(x=\frac{1}{4}\) into the equation)
\(\frac{1}{3} = \frac{\frac{1}{4}+z}{1}\)
\(z = \frac{1}{3} - \frac{1}{4} = \frac{1}{12}\)
Finding B's Work Rate:
Now that we have the work rate of C (\(z = \frac{1}{12}\)), we can find the work rate of B:
\(y = \frac{1}{3} - z = \frac{1}{3} - \frac{1}{12} = \frac{1}{4}\).
Time taken by B to do the work alone:
Since B's work rate is \(\frac{1}{4}\), it will take B 4 hours to complete the work alone.
Therefore, the correct answer is option C) 12 hours.
- A can do the work in 4 hours
- B and C together can do the work in 3 hours
- A and C together can do the work in 2 hours
Work Rates:
Let the work rate of A be \(x\), work rate of B be \(y\), and work rate of C be \(z\).
Calculating Work Rates:
- Since A can do the work in 4 hours, A's work rate is \(\frac{1}{4} = \frac{x}{1}\) which implies \(x = \frac{1}{4}\).
- From the given data, we know that B and C together can do the work in 3 hours. Their combined work rate is \(\frac{1}{3} = \frac{y+z}{1}\).
- Similarly, A and C together can do the work in 2 hours. Their combined work rate is \(\frac{1}{2} = \frac{x+z}{1}\).
Solving the Equations:
Substitute the values of \(x\) and \(y\) into the equations above to find the value of \(z\).
\(\frac{1}{3} = \frac{\frac{1}{4}+z}{1}\) (Substitute \(x=\frac{1}{4}\) into the equation)
\(\frac{1}{3} = \frac{\frac{1}{4}+z}{1}\)
\(z = \frac{1}{3} - \frac{1}{4} = \frac{1}{12}\)
Finding B's Work Rate:
Now that we have the work rate of C (\(z = \frac{1}{12}\)), we can find the work rate of B:
\(y = \frac{1}{3} - z = \frac{1}{3} - \frac{1}{12} = \frac{1}{4}\).
Time taken by B to do the work alone:
Since B's work rate is \(\frac{1}{4}\), it will take B 4 hours to complete the work alone.
Therefore, the correct answer is option C) 12 hours.
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