Calculating Combined Work Time for A and B
This problem involves calculating the time required for two individuals, A and B, to complete a work together based on their individual work rates and contributions.
Step 1: Determine A's Work Rate
A can complete a piece of work in 60 days. This means A's work rate is:
$ \text{Rate}_A = \frac{1}{60} \text{ of the work per day} $
Step 2: Calculate Work Done by A
A worked for 15 days. The portion of the work A completed is:
$ \text{Work done by A} = \text{Rate}_A \times \text{Days worked} = \frac{1}{60} \times 15 = \frac{15}{60} = \frac{1}{4} \text{ of the work} $
Step 3: Calculate Remaining Work
The amount of work left after A worked is:
$ \text{Remaining Work} = 1 - \text{Work done by A} = 1 - \frac{1}{4} = \frac{3}{4} \text{ of the work} $
Step 4: Determine B's Work Rate
B finished the remaining 3/4 of the work in 30 days. B's work rate is calculated as:
$ \text{Rate}_B = \frac{\text{Remaining Work}}{\text{Days taken by B}} = \frac{3/4}{30} = \frac{3}{4 \times 30} = \frac{3}{120} = \frac{1}{40} \text{ of the work per day} $
Step 5: Calculate Combined Work Rate
When A and B work together, their combined work rate is the sum of their individual rates:
$ \text{Combined Rate} = \text{Rate}_A + \text{Rate}_B = \frac{1}{60} + \frac{1}{40} $
Find a common denominator (LCM of 60 and 40 is 120):
$ \text{Combined Rate} = \frac{2}{120} + \frac{3}{120} = \frac{5}{120} = \frac{1}{24} \text{ of the work per day} $
Step 6: Calculate Time Taken Together
The total time required to complete the work together is the reciprocal of their combined work rate:
$ \text{Time Together} = \frac{\text{Total Work}}{\text{Combined Rate}} = \frac{1}{1/24} = 24 \text{ days} $
Thus, if A and B work together, they will complete the work in 24 days.
Similar Questions
- A can lay railway track between two given stations in 22 days and B can do the same job in 10 days. With the help of C, they did the job in 2 days only. Then, C alone can do the job in
- Anjani can do a certain piece of work in 24 days. Anjani and Khushbu can together do the same work in 12 days, and Anjani, Khushbu and Sushmita can do the same work together in 9 days. In how many days can Anjani and Sushmita do the same work together?
- 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?
- A can lay railway track between two given stations in 21 days and B can do the same job in 16 days. With the help of C, they did the job in 2 days only. Then, C alone can do the job in
- Working $5\text{ h}$ a day, A can complete a task in $8\text{ days}$ and working $6\text{ h}$ a day, B can complete the same task in $10\text{ days}$. Working $8\text{ h}$ a day, they can jointly complete the task in:
- A does half as much work as B in three-fourth of the time taken by B. If together they take $12\text{ days}$ to complete the work, how much time shall B take to do it alone?
- A is only $40\%$ as efficient as B. C is $50\%$ as efficient as A and B together. If C alone completes the task in $30\text{ days}$, then A, B and C together can complete the task in:
- If 24 persons can complete a task in 5 days, in how many days, 6 persons would be able to complete it?
- 15 men or 25 women can reap a field in 22 days. How many days will 9 men and 18 women take to reap it?
- 4 men can complete a piece of work in 18 days, while 9 women can do it in 8 days. In how many days can 3 women and 6 men complete this work?
Important Questions from Time and Work
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 ∶ 2. In how many days 6 men and 2 women together can do the same work?
Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?
Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?
