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# Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone.

Last updated date: 18th Mar 2023
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Hint: Express the work done by both in the form of an equation according to the given condition and solve the equation.

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.