Answer
Verified
478.5k+ views
Hint: Express the work done by both in the form of an equation according to the given condition and solve the equation.
Complete step-by-step answer:
In the question it is given that Pintu takes 6 days more than those of Nishu to complete the work
So let's take the no of days taken by Nishu to complete the work=x
So, the number of days taken by Pintu=x+6
So, the amount of work done by Nishu in 1 day=$\dfrac{1}{x}$
The amount of work done by Pintu in 1 day=$\dfrac{1}{{x + 6}}$
So, both of them work together to finish a work in 4 days,
So we can write $\dfrac{1}{x}$+$\dfrac{1}{{x + 6}}$=$\dfrac{1}{4}$
$
\Rightarrow \dfrac{{x + 6 + x}}{{{x^2} + 6x}} = \dfrac{1}{4} \\
\Rightarrow 8x + 24 = {x^2} + 6x \\
\Rightarrow {x^2} - 2x - 24 = 0 \\
\\
$
This is in the form of a quadratic equation,
So let us solve this and find out the roots
$
\Rightarrow {x^2} - 6x + 4x - 24 = 0 \\
\Rightarrow x(x - 6) + 4(x - 6) = 0 \\
\Rightarrow x = 6,x = - 4 \\
$
Since , the number of days cannot be negative, so we can write x=6
So, the number of days taken by Nishu to complete the work=6 days
The number of days taken by Pintu to complete the work=x+6=6+6=12 days.
Note: Here we have to find out the value of both x and x+6 and shouldn’t stop the solution after finding the value of only x.
Complete step-by-step answer:
In the question it is given that Pintu takes 6 days more than those of Nishu to complete the work
So let's take the no of days taken by Nishu to complete the work=x
So, the number of days taken by Pintu=x+6
So, the amount of work done by Nishu in 1 day=$\dfrac{1}{x}$
The amount of work done by Pintu in 1 day=$\dfrac{1}{{x + 6}}$
So, both of them work together to finish a work in 4 days,
So we can write $\dfrac{1}{x}$+$\dfrac{1}{{x + 6}}$=$\dfrac{1}{4}$
$
\Rightarrow \dfrac{{x + 6 + x}}{{{x^2} + 6x}} = \dfrac{1}{4} \\
\Rightarrow 8x + 24 = {x^2} + 6x \\
\Rightarrow {x^2} - 2x - 24 = 0 \\
\\
$
This is in the form of a quadratic equation,
So let us solve this and find out the roots
$
\Rightarrow {x^2} - 6x + 4x - 24 = 0 \\
\Rightarrow x(x - 6) + 4(x - 6) = 0 \\
\Rightarrow x = 6,x = - 4 \\
$
Since , the number of days cannot be negative, so we can write x=6
So, the number of days taken by Nishu to complete the work=6 days
The number of days taken by Pintu to complete the work=x+6=6+6=12 days.
Note: Here we have to find out the value of both x and x+6 and shouldn’t stop the solution after finding the value of only x.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE