Answer
361.3k+ views
Hint: In this type of question where men and women together perform a work. The first thing is to assume the one day work of a woman and one day work of a man will be x and y respectively. After this form the two equations in two variables using the given data in question.
Complete step-by-step solution -
In the question, it is given that a certain amount of work is completed by 2 women and 5 men in 4 days, while 3 women and 6 men can finish the same work in 3 days. And we have to find time taken if 1 woman or 1 man alone does the work.
So first let us assume that one day work of one woman = x
And one day work of a man = y
It is given that time taken by 2 women and 5 men to complete a work= 4 days
$\therefore $ In one day work done by 2 women and 5 men= $\dfrac{1}{4}$
So using the above information, we can write:
$
{\text{2x + 5y = }}\dfrac{1}{4} \\
\Rightarrow 4\left( {{\text{2x + 5y}}} \right) = 1 \\
$
$ \Rightarrow 8{\text{x + 20y = 1}}$ _______________________ (1)
It is given that time taken by 3 women and 6 men to complete a work= 3 days
$\therefore $ In one day work done by 3 women and 6 men= $\dfrac{1}{3}$
So using the above information, we can write:
$
{\text{3x + 6y = }}\dfrac{1}{3} \\
\Rightarrow 3\left( {{\text{3x + 6y}}} \right) = 1 \\
$
$ \Rightarrow 9{\text{x + 18y = 1}}$ _________________ (2)
Multiplying equation 2 by 10 and equation 1 by 9, we get:
72x+180y = 9 _______________________ (3)
And
90x+180y = 10 ______________________ (4)
Now on subtracting equation 3 from equation 4, we get:
18x=1
$ \Rightarrow {\text{x = }}\dfrac{1}{{18}}$
Putting the value of x in equation 2, we get:
y =$\dfrac{1}{{36}}$ .
So the work done by 1 woman in 1 day = $\dfrac{1}{{18}}$
$\therefore $ Time taken by 1 woman to complete the whole work =$\dfrac{1}{{\dfrac{1}{{18}}}} = 18$ days.
Similarly, the work done by 1 man in 1 day = $\dfrac{1}{{36}}$
$\therefore $ Time taken by 1 man to complete the whole work =$\dfrac{1}{{\dfrac{1}{{36}}}} = 36$ days.
Note: In this type of question, first you should know how to calculate work done in one day by 1 person. After this form the equations using the given information in terms of variable x and y. After getting the values of x and y just divide the values of x and y by 1 to get the time taken by 1 person to complete the whole work.
Complete step-by-step solution -
In the question, it is given that a certain amount of work is completed by 2 women and 5 men in 4 days, while 3 women and 6 men can finish the same work in 3 days. And we have to find time taken if 1 woman or 1 man alone does the work.
So first let us assume that one day work of one woman = x
And one day work of a man = y
It is given that time taken by 2 women and 5 men to complete a work= 4 days
$\therefore $ In one day work done by 2 women and 5 men= $\dfrac{1}{4}$
So using the above information, we can write:
$
{\text{2x + 5y = }}\dfrac{1}{4} \\
\Rightarrow 4\left( {{\text{2x + 5y}}} \right) = 1 \\
$
$ \Rightarrow 8{\text{x + 20y = 1}}$ _______________________ (1)
It is given that time taken by 3 women and 6 men to complete a work= 3 days
$\therefore $ In one day work done by 3 women and 6 men= $\dfrac{1}{3}$
So using the above information, we can write:
$
{\text{3x + 6y = }}\dfrac{1}{3} \\
\Rightarrow 3\left( {{\text{3x + 6y}}} \right) = 1 \\
$
$ \Rightarrow 9{\text{x + 18y = 1}}$ _________________ (2)
Multiplying equation 2 by 10 and equation 1 by 9, we get:
72x+180y = 9 _______________________ (3)
And
90x+180y = 10 ______________________ (4)
Now on subtracting equation 3 from equation 4, we get:
18x=1
$ \Rightarrow {\text{x = }}\dfrac{1}{{18}}$
Putting the value of x in equation 2, we get:
y =$\dfrac{1}{{36}}$ .
So the work done by 1 woman in 1 day = $\dfrac{1}{{18}}$
$\therefore $ Time taken by 1 woman to complete the whole work =$\dfrac{1}{{\dfrac{1}{{18}}}} = 18$ days.
Similarly, the work done by 1 man in 1 day = $\dfrac{1}{{36}}$
$\therefore $ Time taken by 1 man to complete the whole work =$\dfrac{1}{{\dfrac{1}{{36}}}} = 36$ days.
Note: In this type of question, first you should know how to calculate work done in one day by 1 person. After this form the equations using the given information in terms of variable x and y. After getting the values of x and y just divide the values of x and y by 1 to get the time taken by 1 person to complete the whole work.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)