Quants 12 - Time and Work

Practice Questions:

Question 1:

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?

Let the total number of workers be  n.
Total number of days to complete the work is 40. If there are 10 workers less, the work will take n+5 days.
This can be formulated as,

40n = 30(n+5)
40n = 30n + 150
10n = 150
n = 15 workers

Question 2:

15 men could finish a piece of work in 210 days. But at the end of 100 days, 15 additional men are employed. In how many more days will the work be complete?

15 men can do the work in 210 days.
By the end of 100 days, there were 15 + 15 men.
Total work = 15 * 210 = 3150 man days
After 100 days, work = 15 * 100 = 1500 days
Work left = 3150 - 1500 = 1650 man days
Work done by 30 men each day = 1650 / 30 = 55 days

Question 3:

24 men working 8 h a day can finish a work in 10 days. Working at a rate of 10 h a day, the number of men required to finish the work in 6 days is ___.

24 men can do the work in 10 days by working 8 hours per day.
Working at 10 hours per day and to complete in 6 days,
24 * 8 * 10 = N * 10 * 6
N = ( 24 * 8 * 10 ) / 10 * 6
N = 32 men

Question 4:

Abbot can do some work in 10 days, Bill can do it in 20 days and Clinton can do it in 40 days. They start working in turns with Abbot starting to work on the first day followed by Bill on the second day and by Clinton on the third day and again by Abbot on the fourth day and so on till the work is completed fully. Find the time taken to complete the work fully?

Abbot = 10 days - 1st day, 4th day and so on = 10% work
Bill = 20 days - 2nd day, 5th day and so on = 5% work
Clinton = 40 days - 3rd day, 6th day and so on = 2.5% work
So, in a set of three days, work done = 10 + 5 + 2.5 % = 17.5% of work
In 15 days, work done = 17.5 * 5 = 87.5 work
Remaining work = 12. 5 %
On 16th day, Abbot will complete 10%
So remaining is 2.5%
On the 17th day, the remaining work will be done in the half day as Bill can do 5%
So, it will take 16.5 days to complete the work fully. 

Question 5:

A certain job was assigned to a group of men to do it in 20 days. But 12 men did not turn up for

the job and the remaining men did the job in 32 days. The original number of men in group was

Let the number of men be n.
Total number of days = 20
12 men didn't turn up. So, the men now is n - 12
The work was completed in 32 days.
Let's formulate the equation as n * 20 = (n-12) * 32
20n = 32n - 384
12n = 384
n = 384 / 12 = 32 men

Time to Think:

In a fort there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?