Understanding Work Rates
This problem involves calculating the time taken by an individual (C) to complete a job, given the times taken by others (A and B) individually and the time taken by all three together.
- The rate of work is the reciprocal of the time taken to complete the job.
- Rate = $\frac{1}{\text{Time}}$
Calculating Individual Work Rates
First, determine the work rate of A and B:
- A's time = 22 days. A's rate = $\frac{1}{22}$ of the job per day.
- B's time = 10 days. B's rate = $\frac{1}{10}$ of the job per day.
Calculating Combined Work Rate (A, B, and C)
The combined time for A, B, and C to complete the job is 2 days. Their combined work rate is:
- Combined rate (A+B+C) = $\frac{1}{2}$ of the job per day.
Finding C's Work Rate
The combined rate is the sum of individual rates: Rate(A+B+C) = Rate(A) + Rate(B) + Rate(C). We can find C's rate by subtracting A's and B's rates from the combined rate.
- Calculate the combined rate of A and B: Rate(A) + Rate(B) = $\frac{1}{22} + \frac{1}{10}$
- Find a common denominator (LCM of 22 and 10 is 110): $\frac{5}{110} + \frac{11}{110} = \frac{16}{110} = \frac{8}{55}$ job per day.
- Calculate C's rate: Rate(C) = Rate(A+B+C) - (Rate(A) + Rate(B)) Rate(C) = $\frac{1}{2} - \frac{8}{55}$
- Find a common denominator (LCM of 2 and 55 is 110): Rate(C) = $\frac{55}{110} - \frac{16}{110} = \frac{39}{110}$ job per day.
Calculating C's Time to Complete the Job
C's time is the reciprocal of C's work rate.
- C's time = $\frac{1}{\text{Rate(C)}} = \frac{1}{\frac{39}{110}}$ days
- C's time = $\frac{110}{39}$ days
Converting to Mixed Fraction
To express $\frac{110}{39}$ as a mixed fraction:
- Divide 110 by 39: $110 \div 39 = 2$ with a remainder of $32$ ($110 = 2 \times 39 + 32$).
- Therefore, C's time = $2 \frac{32}{39}$ days.
Similar Questions
- Hema can do a certain piece of work in 30 days. Hema and Raji can together do the same work in 22 days, and Hema, Raji and Smitha can do the same work together in 15 days. In how many days can Hema and Smitha do the same work together?
- John, Johnny and Janardan can finish a task in a field in 6, 12, and 24 days, respectively. In how many days will they finish the task working together?
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- Sita can clean a hotel in 20 days. Rita can clean the same hotel in 30 days. How many days will they take to clean the hotel together?
- A, B and C can complete a task in 36, 54 and 72 days respectively. Together they started the task but A left 8 days before the completion of the task while B left 12 days before the completion. The number of days for which C worked is:
- A alone can complete $\frac{2}{5}$ of a task in 12 days, while B alone can complete $\frac{3}{4}$ of the same task in 25 days. In how many days can they complete the task if they work together?
- If A, B and C can complete a task alone in 15 days, 20 days and 25 days, respectively, then in how many days can they complete the same task if they work together?
- A and B working alone can finish a task in 12 and 16 days respectively. In how many days can the task be finished if they work for one day each alternatively, and A begins the work?
- Reena and Jaya can complete a piece of work in 6 days and Jaya alone can complete it in 8 days. In how many days can Reena alone complete it?
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Important Questions from Time and Work
Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?
A tank is filled in 8 hours by three taps A, B and C. The tap C is thrice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?
Had been one menless, then the number of days required to do a piece of work would have been one more. If the number of Man. Days required to complete the work is 56, how many workers were there?
A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it 12 hours. How long will B alone take to do it?
- lf 12 men can do a work in 20 days, in how many days will the work be done by 15 men-
