Work and Time Problem Analysis
This problem involves calculating the time required to complete a task when the number of workers changes. It demonstrates an inverse relationship between the number of workers and the time taken.
Calculating Days Needed
Let the number of boys be $B$ and the number of days be $D$. The total work done is constant. We can represent this relationship as:
$ B_1 \times D_1 = B_2 \times D_2 $
Where:
- $B_1$ = Initial number of boys = 15
- $D_1$ = Initial number of days = 20
- $B_2$ = Final number of boys = 20
- $D_2$ = Final number of days = ?
Step-by-Step Calculation
- Substitute the known values into the formula:
$ 15 \times 20 = 20 \times D_2 $
- Calculate the product on the left side:
$ 300 = 20 \times D_2 $
- Solve for $D_2$ by dividing both sides by 20:
$ D_2 = \frac{300}{20} $
$ D_2 = 15 $
Therefore, 20 boys can complete the same work in 15 days.
Similar Questions
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 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?
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 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 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, 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?
If 6 machines complete a task in 10 days, how many days for 15 machines at the same rate?
A and B can finish a certain job in 28 and 35 days, respectively. They started working together, but A left after a while, and B managed to complete the remaining work in 17 days. How many days did A work before leaving?
A can lay railway track between two specified stations in 16 days, while B can complete the same task in 12 days. When C assists them, they manage to finish the job in just 4 days. How long would it take for C to complete the job on their own?
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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-
