Dear Reader, Below are three problems based on work and time.
Question 1
In a Construction Company, due to the lack of labourers, the output of the company decreases by 44%. By what percentage the number of labourers that should be increased so that the production remains the same as earlier?
a) 72.5% b)56% c)78.5% d) none of these.
Answer : c) 78.5%
Solution :
In current conditions only 56% work only has been completed. (100% - 44%)
Let L number of labourers are present currently in the company. Then these L people are responsible for 56% of work.
Labourers % of Work L 56 ? 100
Number of Labourers required to complete 100% of work = 100L/56 = 1.7857L
Required Increase in the number of labourers = Number of Labourers Required To Complete 100% of work - Original Number of Labourers = 1.7857L - L = .7857L
Percentage increase in the number of labourers = Required Increase in the number of labourers / Original Number of Labourers x 100 = .7857L /L x 100 = 78.57%
Question 2
An event management Company wanted to complete its pending work. 4 women and 12 men together can complete a piece of work in four days.. How many days will four men alone take to complete the piece of work if two women alone can complete the piece of work in 16 days?
a) 32 b) 24 c) 16 d) 12
Answer : b) 24 days.
Solution :
2 women can complete the work in 16 days.
Hence 4 women can complete the work in 8 days. But it is given that 4 women and 12 men complete the work in 4 days. This means that addition of 12 men to workforce has reduced the number of working days to 4 which is exactly half of 8 days that 4 women alone would had taken. Logically this is possible only when 12 men's work per day is equal to 4 women's work per day.
4 women's work = 12 men's work
Dividing by 4 on both sides,
1 woman's work = 3 men's work. -> eq 1
Now, as given, we know that 4 women + 12 men can complete the work in 4 days.
Applying eq 1 in the above statement we get,
4 x 3 men + 12 men can complete the work in 4 days
24 men can complete the work in 4 days.
If 24 men is replaced by just one man, he has to do all the work alone and he would take 24 times more number of days then that would had consumed by 24 men working together.
Therefore, 1 man can complete the work in 4 x 24 = 96 days.
Now, if this one man is replaced by 4 men working together, there will be four people to share the work and hence the time taken would be reduced by 4 times than it would had taken by one man working alone.
Therefore, four men can complete the work in 96 / 4 days = 24 days.
Question 3
In a media management company 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days. Find the time taken by 15 men and 20 boys in doing the same type of work?
a)4 days b) 5 days c) 6 days d) 7 days
Answer : a) 4 days.
Solution :
Let one man’s work for one day be x and
Let one boy’s work for one day be y
Then 6x + 8 y = 1/10 -> eq 1
26x + 48 y = 1/2 -> eq 2
Multiply eq 1 by 6 on both sides :
36x + 48 y = 3/5 -> eq 3
eq 3 - eq 2 :
36x + 48y - 26x + 48y = 3/5 - 1/2
10x = 1/10 So x = 1/100 and y = 1/200
Amount of work that can be done by15 men and 20 boys in one day = (15/100 + 20/200) = 1/4
Therefore 15 men and 20 boys can do the work in 4 days.