Discussion

Explanation:

Let the time A and B take while working together be ‘x’ days.

As per question $\frac{1}{\mathrm{x}+8}+\frac{1}{\mathrm{x}+\frac{9}{2}}=\frac{1}{\mathrm{x}}$

or, $\frac{\mathrm{x}+25∕2}{\left(\mathrm{x}+8\right)\left(\mathrm{x}+\frac{9}{2}\right)}=\frac{1}{\mathrm{x}}$

$2{\mathrm{x}}^2+\frac{25}{2}\mathrm{x}$ = ${\mathrm{x}}^2+\frac{25}{2}\mathrm{x}+36$

x² = 36

⇒ x = 6 days

Remember:
Solution for an equation of the form $\frac{1}{x+a}$ + $\frac{1}{x+b}$ = $\frac{1}{x}$

is x = $\sqrt{a\times b}$

Hence, option (a).

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