From past few days, we have been working on providing study materials for various topics on our Blog. Few days back, we wrote on Verbal reasoning (Syllogisms) and we hope it was beneficial for all. This blog on ‘Time and Work’ is the next in series.
Problems on ‘Time and Work’ are a common feature in most of the Bank exams. If you are well versed with the basics and have practiced these problems during your preparation, they give you an easy opportunity to score and also save time. Here, I will try and explain you the basic fundas with the help of examples. Let us start with a very basic problem:
Problem 1: A takes 5 days to complete a piece of work and B takes 15 days to complete a piece of work. In how many days can A and B complete the work if they work together?
Standard Solution: Let us consider Work to be 1 unit. So if W = 1 Unit and A takes 5 days to complete the work then in 1 day A completes 1/5th of the work. Similarly B completes 1/15th of the work.
If they work together, in one day A and B can complete (1/5 + 1/15 = 4/15) of the work. So to complete 1 unit of work they will take 15/4 days.
Let us assume that there are 15 days (LCM of 5 and 15).
A will do 3 times of work in 15 days and B will do 1 times of work in 15 days.
Together, A & B will do 4 times work in 15 days.
Therefore, 1 times work will be done in 15/4 days.
Problem 2: X can do a work in 15 days. After working for 3 days he is joined by Y. If they complete the remaining work in 3 more days, in how many days can Y alone complete the work?
In 6 days, X will do 6/15 = 2/5 times work.
In 3 days, Y does (1-2/5) = 3/5 times work.
Therefore, to do 1 times work, Y will take 3÷(3/5) = 5 days
Problem 3: If 10 men take 15 days to complete a work. In how many days will 25 men complete the work?
Solution: Given that 10 men take 15 days to complete the work. So the number of man-days required to complete the work = 10 * 15 man-days. So, assume W = 150 man-days.
Now the work has to be done by 25 men and since W = 150 man-days, the number of days to complete the work would be 150/25 = 6 days.
Or 10 * 15 = 25 * No. of days => No. of days = 6
Problem 4: A piece of work can be done by 8 boys in 4 days working 6 hours a day. How many boys are needed to complete another work which is three times the first one in 24 days working 8 hours a day?
Solution: Assume the first piece of work to be 8 * 4 * 6 = 192 boy-day-hours.
The second piece of work = 3 (The first piece of work) = 3 * 192 = 576 boy-day-hours. So W = 576 boy-day-hours.
If this work has to be completed in 24 days by working 8 hours a day the number of boys required would be 576/(24 * 8) = 3 boys.
Or 3 * 8 * 4 * 6 = 24 * 8 * No. of boys => No. of boys = 3
Problem 5: X can do a piece of work in 20 days and Y can do the same work in 30 days. They finished the work with the help of Z in 8 days. If they earned a total of Rs. 5550, then what is the share of Z?
Let us assume that there are 120 days (LCM of 20, 30 and 8).
X can do 6 times work in 120 days, Y can do 4 times work in 12 days.
(X + Y + Z) can do 15 times work in 120 days.
Therefore, Z can do 5 (= 15 – 6 – 4) times work in 120 days. Hence, Z can do 1 times work in 120/4 = 24 days.
Share of Z = Work done by Z in 8 days * Total earnings
= (8/24) * 5550
= Rs. 1850
We would suggest to practice ‘Time and Work’ problems by LCM method as it saves lot of time, which during exams might be very beneficial.