A and B Work Rates Calculation
First, calculate the time each person takes to complete the entire task and their respective daily work rates.
- Person A: Completes $\frac{2}{5}$ of the task in 12 days.
- Time for A to complete the whole task = $12 \div \frac{2}{5} = 12 \times \frac{5}{2} = 30$ days.
- A's daily work rate = $\frac{1}{30}$ of the task per day.
- Person B: Completes $\frac{3}{4}$ of the task in 25 days.
- Time for B to complete the whole task = $25 \div \frac{3}{4} = 25 \times \frac{4}{3} = \frac{100}{3}$ days.
- B's daily work rate = $\frac{1}{\frac{100}{3}} = \frac{3}{100}$ of the task per day.
Combined Work Rate Calculation
Determine their combined daily work rate by adding their individual rates.
- Combined daily work rate = A's rate + B's rate
- Combined rate = $\frac{1}{30} + \frac{3}{100}$
- Find a common denominator (LCM of 30 and 100 is 300).
- Combined rate = $\frac{1 \times 10}{30 \times 10} + \frac{3 \times 3}{100 \times 3} = \frac{10}{300} + \frac{9}{300} = \frac{19}{300}$ of the task per day.
Task Completion Time Together
Calculate the total time needed to complete the task when they work together. This is the reciprocal of their combined daily work rate.
- Time together = $\frac{1}{\text{Combined rate}}$
- Time together = $\frac{1}{\frac{19}{300}} = \frac{300}{19}$ days.
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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?
