TIME & WORK
In the context of the PSA, you have to understand the following basic concepts of this chapter:
If A does a work in a days, then in one day A does
In the above case, we take the total work to be done as “1 unit of work”. Hence, the work will be completed when 1 unit of work is completed.
For example, if A can do a work in 10 days and B can do the same work in 12 days, then the work will be completed in how many days.
Ex. 1 A contractor undertakes to build a wall in 50 days. He employs 50 people for the same. However, after 25 days he finds
that the work is only 40% complete. How many more men need to be employed to :
(a) Complete the work in time ?
S ol. In order to complete the work in time, the contractor has to finish the remaining 60% of the work in 25 days.
Now, in the first 25 days the work done = 50 × 25 = 1250 man-days ® 40% of the work.
Hence, work left = 60% of the work = 1875 man-days. Since, 25 days are left to complete the task, the number of people required is 1875/25 = 75 men.
Since, 50 men are already working, 25 more men are needed to complete the work.
Thought process should go like: 1250 ® 40% of work.
Hence, 1875 men-days required to complete the work.
Since there are only 25 days left, we need 1875/25 = 75 men to complete the work.
(b) Complete the work 10 days before time ?
For this purpose, we have to do 1875 man-days of work in 15 days. Hence, men = 1875/15 = 125 men.
Ex. 2 For the previous problem, if the contractor continues with the same workforce:
(a) how many days behind schedule will the work be finished ?
Sol. He has completed 40% work in 25 days. Hence, to completed the remaining 60% of the work, he would required 50% more days (i.e. 37.5 days) (Since, 60% is 1.5 times of 40%)
Hence, the work would be done 12.5 days behind schedule.
(b) how much increase in efficiency is required from the work force to completed the work in time?
Sol. If the number of men working is kept constant, the only way to finish the work in time is by increasing the efficiency so that more work is done every man-day.
This should be mathematically looked at as follows: Suppose, that 1 man-day takes care of 1 unit of work. Then, in the first 25 days, work done = 25
(days) × 50 (men) × 1 (work unit per man-day) = 1250 units of work. Now, this 1250 units of work is just 40% of the work. Hence, work left = 1875 unit of work.
Then, 25 (days) × 50 (men) × z (work units per man-day) = 1875 ® z = 1.5
Thus, the work done per man-day has to rise from 1 to 1.5, that is, by 50%. Hence, the efficiency of work has to rise by 50%.
Ex. 3 A is twice as efficient as B. If they complete a work in 30 days find the times required by each to complete the work individually.
Sol. When we say that A is twice as efficient as B, it means that A takes half the time that B takes to complete the same work.
Thus, if we denote A’s 1 days’ work as A and B’s one day’s work as B, we have A = 2B
Then, using the information in the problem, we have : 30 A + 30 B = 100% work
That is, 90 B = 100% work ® B = 1.11% (is the work done by B in 1 day) ® B requires 90 days to complete the work alone.
Since, A = 2B ® we have A = 2.22% ® A requires 45 days to do the work alone.
You should be able to solve this mentally with the following thought process while reading for teh first time:
ASSIGNMENT
1. Raju can do 25% of a piece of work in 5 days. How many days will he take to complete the work ten times ?
(A) 150 days (B) 250 days (C) 200 days (D) 180 days (E) 192 days
2. 6 men can do a piece of work in 12 days. How many men are needed to do the work in 18 days.
(A) 3 men (B) 6 men (C) 4 men (D) 2 men (E) 5 men
3. A can do a piece of work in 20 days and B can do it in 15 days. How long will they take if both work together ?
4. In question 3 if C, who can finish the same work in 25 days, joins them, then how long will they take to complete the work ?
5. Nishu and Archana can do a piece of work in 10 days and Nishu alone can do it in 12 days. In how many days can Archana do it alone ?
(A) 60 days (B) 30 days (C) 50 days (D) 45 days (E) 52 days
6. Apurva can do a piece of work in 12 days. Apurva and Amit complete the work together and were paid Rs. 54 and Rs. 81 respectively. How many days must they have taken to copmplete the work together ?
(A) 4 days (B) 4.5 days (C) 4.8 days (D) 5 days (E) 4.2 days
7. Raju is twice as good as Vijay. Together, they finish the work in 14 days. In how many days can Vijay alone do the same work ?
(A) 16 days (B) 21 days
(C) 32 days (D) 72 days
(E) 42 days
8. In a company XYZ Ltd. a certain number of engineers can develop a design in 40 days. If there were 5 more engineers, it could be finished in 10 days less. How many engineers were there in the beginning ?
(A) 18 (B) 20
(C) 25 (D) 15
(E) 16
9. If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days, compare the daily work done by a man with that done by a boy ?
(A) 1 : 2 (B) 1 : 3
(C) 2 : 1 (D) 3 : 1
(E) 3 : 2
10. A can do a work in 10 days and B can do the same work in 20 days. They work together for 5 days and then A goes away. In how many more days will B finish the work ?
ANSWER KEY
1) C 2) C 3) B 4) A 5) A 6) A 7) E 8) D 9) C 10) A