Work and Time: Finding B's Time for 3/4 Work
We are given that A and B together can complete a piece of work in 21 days. A alone can complete the same work in 28 days. We need to find the time B takes to complete three-fourth ($ \frac{3}{4} $) of the work.
Calculating Individual Work Rates
- Let the total work be represented by 1 unit.
- Combined work rate of A and B = $ \frac{1 \text{ work}}{21 \text{ days}} $.
- A's work rate = $ \frac{1 \text{ work}}{28 \text{ days}} $.
Determining B's Work Rate
To find B's individual work rate, we subtract A's rate from the combined rate:
B's work rate = (A and B's combined rate) - (A's rate)
B's work rate = $ \frac{1}{21} - \frac{1}{28} $ work per day.
To subtract these fractions, we find the least common multiple (LCM) of 21 and 28, which is 84.
B's work rate = $ \frac{4}{84} - \frac{3}{84} = \frac{1}{84} $ work per day.
Calculating Time for B to Complete 3/4 Work
This means B completes $ \frac{1}{84} $ of the work each day. Therefore, B takes 84 days to complete the entire work.
We need to find the time B takes to complete only three-fourth ($ \frac{3}{4} $) of the work.
Time for B to do $ \frac{3}{4} $ work = $ \frac{3}{4} \times (\text{Time for B to do full work}) $
Time = $ \frac{3}{4} \times 84 $ days
Time = $ 3 \times \frac{84}{4} $ days
Time = $ 3 \times 21 $ days
Time = 63 days.
Thus, B alone can do three-fourth of the same work in 63 days.
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?
