Question

The sum of one fifth, one third and one ninth of a number is $29$. Find the number.

• A. $45$
• B. $29$
• C. $54$
• D. None of the above.

Answer 1

The correct option is A $45$

Let the required number be $x$

According to the question, $\frac{x}{5}+\frac{x}{3}+\frac{x}{9}=29$

L.C.M of $5,3,9$ is $45.$
Then the equation becomes :
$\frac{x\times 9}{5\times 9}+\frac{x\times 15}{3\times 15}+\frac{x\times 5}{9\times 5}=29$

$⟹\frac{9x+15x+5x}{45}=29$

$⟹29x=29\times 45$

$⟹x=\frac{29\times 45}{29}$

$\therefore x=45$