Question

Aditya takes 9 days more than his father to do a certain piece of work . Together they can do the work in 6 days. How many days will Aditya take to do that work alone.
PLZ PLZ answer std 10 from quadratic equations chapter..

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• Aditya takes 9 more days than his father to do a piece of work.

• He and his father together can do the work in 6 days.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The number of days, Aditya take to do that work alone.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the number of days Aditya takes to do the work be x

And number of days taken by his father be y

As Aditya takes 9 more days than his father to complete the work.

$\rm \implies x - y = 9$

$\rm \implies x =y + 9......(i)$

$\rm Aditya's \: one \: day \: work = \dfrac{1}{x}$

$\rm His \: father's \: one \: day \: work = \dfrac{1}{y}$

They together take 6 days to complete the work.

$\implies \rm \dfrac{1}{x} + \dfrac{1}{y} =\dfrac{1}{6}$

$\implies \rm \dfrac{y + x}{xy} =\dfrac{1}{6}$

$\implies \rm y + x =\dfrac{xy}{6}$

$\implies \rm 6(x + y ) ={xy}$

From (i) x = y + 9

$\implies \rm 6(y + 9 + y ) ={y(y + 9)}$

$\implies \rm 6(2y + 9 ) ={y(y + 9)}$

$\implies \rm 12y + 54 = {y}^{2} + 9y$

$\implies \rm {y}^{2} + 9y - 12y - 54 = 0$

$\implies \rm {y}^{2} - 3y - 54 = 0$

$\implies \rm {y}^{2} - 9y + 6y - 54 = 0[/tex</p><p></p><p>[tex]\implies \rm {y}(y - 9) + 6(y - 9) = 0$

$\implies \rm (y - 9) (y + 6) = 0$

$\implies \rm y = 9 \: , \: - 6$

Since the number of days should not be negative.

$\implies \rm y = 9$

Since:-

$\implies \rm x - y = 9$

$\implies \rm x - 9= 9$

$\implies \rm x = 18$

Hence;

$\boxed{ \therefore \rm \: Aditya \: can \: complete \: the \: work \: in \: 18 \: days}$

Answer 2

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$\huge\red{\underline{{\bf Question : }}}$

Aditya takes 9 days more than his father to do a certain piece of work. Together they can do the work in 6 days. How many days will Aditya take to do that work alone.

$\huge\red{\underline{{\bf Answer : }}}$

$\large\sf\underline\green{Given:}$

➛ Aditya takes 9 days more than his father to do a certain piece of work .

➛ Together they can do the work in 6 days.

$\large\sf\underline\green{To\: Find:}$

➛ How many days will Aditya take to do that work alone.

$\large\sf\underline\green{Solution:}$

➛ Let aditya can do work in x days.

➛ Let his father can do work in y days.

➛ Then,

x - y = 9 OR x = 9 + y

➛ Aditya's one day work = 1/x

➛ Father's one day work = 1/y

➛ Then,

☞ $\sf\blue{\frac{1}{x} + \frac{1}{y} = \frac{1}{6} }$

☞ $\sf\blue{ \frac{x + y}{xy} = \frac{1}{6} }$

☞ $\sf\blue{xy = 6(x + y)}$

☞ $\sf\blue{y(9 + y) = 6(9 + y + y)}$

☞ $\sf\blue{9y + {y}^{2} = 54 + 12y}$

☞ $\sf\blue{{y}^{2} - 3y - 54 = 0}$

☞ $\sf\blue{y = \frac{3 + \sqrt{9 + 216} }{2} }$

☞ $\sf\blue{y = \frac{3 + 15}{2} }$

☞ $\sf\blue{y = 9, - 6}$

☞ $\sf\blue{x = 9 + y = 9 + 9 = 18 \: days}$

➛ Hence, Aditya can complete work in 30 days.

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