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The number of solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{6}$ where $x, y \in N$

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Correct option is A

1x+1y=16⇒6(x+y)=xy⇒(x−6)(y−6)=36⇒(x−6)∣36.⇒x−6=1,2,3,4,6,9,12,18,36⇒(x,y)=(7,42),(8,24),(9,18),(10,15),(12,12), (15,10),(18,9),(24,8),(42,7)

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The number of solutions of 1x+1y=16 where x,y∈N

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The number of solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{6}$ where $x, y \in N$