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

1.	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» 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 $\implies \rm 6(y + 9 + y ) ={y(y + 9)}$ $\implies \rm 6(2y + 9 ) ={y(y + 9)}$ $\implies \rm 12y + 54 = {y}^{2} + 9y$ $\implies \rm {y}^{2} + 9y - 12y - 54 = 0$ $\implies \rm {y}^{2} - 3y - 54 = 0$ $\implies \rm {y}^{2} - 9y + 6y - 54 = 0[/tex[tex]\implies \rm {y}(y - 9) + 6(y - 9) = 0$ $\implies \rm (y - 9) (y + 6) = 0$ $\implies \rm y = 9 \: , \: - 6$ 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; $\boxed{ \therefore \rm \: Aditya \: can \: complete \: the \: work \: in \: 18 \: days}$