Question

A man and a boy working together can complete a work in 24 days, if for the last 6 days, the man alone does the work, then it is completed in 26 days, how long will the boy complete the work alone?
A. 72 days
B. 20 days
C. 24 days
D. 36 days

Answer 1

Hint: In this question it is given that a man and a boy working together can complete a work in 24 days, if for the last 6 days, the man alone does the work, then it is completed in 26 days, then we have to find how long will the boy complete the work. So to find the solution we have to consider that,
men's 1 day’s work = x and boy's 1 day’s work = y
After finding the values of x and y we are able to find the time taken by the boy in doing the same type of work, i.e the value of $$\dfrac{1}{y}$$.

Complete step-by-step answer:
Let, men’s 1 day’s work = x and boy’s 1 day’s work =y
It is given that a man and a boy working together can complete a work in 24 days,
Therefore, the man can do a work in 24 days =24x,
The boy can do a work in 24 days = 24y
Then, they together can do a work in 24 days = (24x+24y) = 24(x+y)
i.e, 24(x+y) = 1 .......(1)
Now, if for the last 6 days, the man alone does the work, then it is completed in 26 days, i.e, the man does the work for 26 days and the do 20 days.
So we can write, they together worked for 20 days and then the man finishes the work by doing extra 6 days,
Therefore, they together can do a work = 20(x+y)+6x
i.e, 20(x+y)+6x = 1……..(2)
So from (1) and (2) we can write,
$$24\left( x+y\right) =20\left( x+y\right) +6x$$
$$\Rightarrow 24x+24y=20x+20y+6x$$
$$\Rightarrow 24x+24y=26x+20y$$
$$\Rightarrow 26x+20y=24x+24y$$
$$\Rightarrow 26x-24x=24y-20y$$
$$\Rightarrow 2x=4y$$
$$\Rightarrow \dfrac{x}{y} =\dfrac{4}{2}$$
$$\Rightarrow \dfrac{x}{y} =2$$
$$\Rightarrow x=2y$$
Now putting the value of ‘x’ in equation (1) ,
$24\left( 2y+y\right) =1$
$$\Rightarrow 24\times 3y=1$$
$$\Rightarrow 72y=1$$
$$\Rightarrow y=\dfrac{1}{72}$$
Therefore, boy’s 1 day’s work = $$\dfrac{1}{72}$$
Which also can be written as,
$$\dfrac{1}{72}$$ work done by a boy in = 1 day
$\therefore$ $$\left( \dfrac{1}{72} \times 72\right) $$ work done by a boy in = $$\left( 1\times 72\right) $$ days.
Which implies, 1 work done by a boy in = 72 days.
Hence the correct option is option A.


Note: So to solve this type of question you need to know the relationship between the time, work and person, which are,
1. Work & Person: Directly proportional to each other, i.e. more work, more person required.
2. Time & Person: Inversely proportional to each other, i.e. more people, less time required.
3. Work & time: Directly proportional each other, i.e. more work, more time required.