Work and Time Calculation
This problem involves calculating the time taken by a boy to complete a work, given combined work rates and individual work rates.
Man's Work Rate
We are given that one man alone can complete the work in 100 days.
The work rate of one man (\(M\)) is the reciprocal of the time taken:
\( M = \frac{1 \text{ work}}{100 \text{ days}} = \frac{1}{100} \text{ work/day} \)
Combined Work Rate
10 men and 15 boys together complete the work in 6 days.
This means their combined work rate is:
\( (10 \times M) + (15 \times B) = \frac{1 \text{ work}}{6 \text{ days}} = \frac{1}{6} \text{ work/day} \)
Where \(B\) is the work rate of one boy.
Calculating Boy's Work Rate
Substitute the known work rate of a man (\(M = \frac{1}{100}\)) into the combined work rate equation:
\( \left(10 \times \frac{1}{100}\right) + (15 \times B) = \frac{1}{6} \)
Simplify the term for 10 men:
\( \frac{10}{100} + 15B = \frac{1}{6} \)
\( \frac{1}{10} + 15B = \frac{1}{6} \)
Now, isolate \(15B\):
\( 15B = \frac{1}{6} - \frac{1}{10} \)
To subtract the fractions, find a common denominator (which is 30):
\( 15B = \frac{5}{30} - \frac{3}{30} \)
\( 15B = \frac{2}{30} = \frac{1}{15} \text{ work/day} \)
Now, find the work rate of a single boy (\(B\)):
\( B = \frac{1}{15 \times 15} = \frac{1}{225} \text{ work/day} \)
Time Taken by a Boy Alone
The time taken by one boy to complete the work is the reciprocal of his work rate:
\( \text{Time for 1 boy} = \frac{1}{B} = \frac{1}{1/225} \)
\( \text{Time for 1 boy} = 225 \text{ days} \)
Therefore, a boy alone will take 225 days to complete the same work.
Similar Questions
Three workers, X, Y, and Z, can complete a certain job in 10 days, 12 days, and 15 days, respectively. Determine the number of days required for them to complete the job when they work together.
If 5 workers, working at the same rate, complete a job in 12 days, how many days will 10 workers take to complete the same job?
- A piece of work can be done by 16 men in 8 days working 12 hours a day. How many men are needed to complete another work, which is three times the first one, in 24 days working 8 hours a day?
- Ajay can do a painting in 12 days. Amit is 70% more efficient than Ajay. What is the number of days Amit would need to finish the same painting?
Important Questions from Time and work
In a circular race on a track of length 2000 m, X and Y start from the same point at the same time in opposite directions at the speeds of 15 km/h and 33 km/h, respectively. After how much time will they meet next?
Which of the following option figures will complete the pattern in the figure given below?
A has completed two-third of a job in 8 days, and B completes the rest of the job in 20 days. In how many days can they together complete the job?
The smallest 4-digit prime number is:
If Anand can do a piece of work in 9 days and Vinod can complete the same work in 6 days, then in how many days will both of them complete it together?
