Question

If three consecutive numbers are divided by 17, 7, 6 respectively and the quotients are added, the result is 13. The second number is

• A. 35

Answer 1

The correct option is A 35
Let the consecutive numbers be $x$, $x+1$ and $x+2$.

According to the question,
$\frac{x}{17}+\frac{x+1}{7}+\frac{x+2}{6}=13$
$\frac{42x+102(x+1)+119(x+2)}{714}=13$
$\frac{263x+340}{714}=13$
$263x+340=13\times 714$
$263x=9282-340$
$263x=8942$
$x=\frac{8942}{263}$
$x=34$

Hence, the first number is 34. Therefore, second number is 35.