Work and Time: Baban's Solo Duration Calculation
This problem involves calculating the time taken by an individual (Baban) to complete a work, given information about the combined work rates of multiple people.
Define Work Rates
Let the rates of work for Athar, Baban, and Chetan be $R_A$, $R_B$, and $R_C$ respectively. The rate signifies the fraction of the work completed per day.
Formulate Equations from the Problem Statement
- "Athar can do a certain work in the same time in which Baban and Chetan together can do it." This means their rates are equal: $ R_A = R_B + R_C $
- "Athar and Baban together could do it in 10 days." Their combined rate is the sum of their individual rates, and they complete the work in 10 days: $ R_A + R_B = \frac{1}{10} $
- "Chetan alone in 50 days." Chetan's individual rate is: $ R_C = \frac{1}{50} $
Solve for Baban's Rate ($R_B$)
We have a system of three equations. Substitute the value of $R_C$ from the third equation into the first equation:
$ R_A = R_B + \frac{1}{50} $Now substitute this expression for $R_A$ into the second equation:
$ \left( R_B + \frac{1}{50} \right) + R_B = \frac{1}{10} $Simplify and solve for $R_B$:
$ 2 R_B + \frac{1}{50} = \frac{1}{10} $ $ 2 R_B = \frac{1}{10} - \frac{1}{50} $Find a common denominator (50) for the subtraction:
$ 2 R_B = \frac{5}{50} - \frac{1}{50} $ $ 2 R_B = \frac{4}{50} $ $ 2 R_B = \frac{2}{25} $ $ R_B = \frac{1}{25} $Calculate Baban's Time
Baban's rate of work is $\frac{1}{25}$ of the work per day. The time taken by Baban alone is the reciprocal of his rate:
$ \text{Time for Baban} = \frac{1}{R_B} = \frac{1}{1/25} = 25 \text{ days} $Similar Questions
A alone can complete a job in 12 days and B alone in 18 days. A and B agree to do the work for ₹7,200. With C's help they finish it in 5 days. How much should C be paid?
A and B can complete a task together in 12 days, while B and C can finish it in 16 days. After A works on it for 5 days and B for 7 days, C takes the remaining 13 days to finish the work. How many days would it take for C to complete the work alone?
A is three times more efficient as a worker than B, which allows A to complete a job in 60 days less than B. If they work together, they can finish the job in:
A, B, and C can complete a certain task in 20, 30, and 60 days respectively. How many days will it take for A to finish the work if he receives help from B and C every third day?
- A can complete a task in 15 days, and B can complete the same task in 20 days. How long will it take them to complete the task together?
A and B can complete a certain task together in 30 days. After A works for 16 days, B is left to finish the remaining work by himself in 44 days. How many days would it take for B to complete the entire task on his own?
A and B can complete a task in 12 days and 18 days, respectively. They begin the work together, but B leaves after 4 days. How many more days will A take to finish the remaining work?
The ratio of the time taken by A and B to complete a task is 3 : 2. If B can complete the task alone in 18 hours, how many hours will they take to complete the task if they work together?
- A contractor employs 15 men to complete a work in 24 days, working 8 hours per day. After six days, he adds five more men but also reduces the working hours to six per day from the seventh day onwards. If all men work with the same efficiency throughout, how many more days will be required to finish the remaining work?
- 6 women and 4 men can complete a work in 10 days, while 4 women and 5 men complete it in 10 days. In how many days will 8 women complete it?
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-
