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
A person can complete 20% of work in 8 days and another person y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?
There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per out of which 5% are unfit for sale. In how many days will the order be completed?
Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?
