Question

Find three consecutive numbers such that if they are divided by $10,17,26$ respectively, the sum of their quotients will be $10$.

Answer 1

Let the consecutive numbers be $x,x+1$ and $x+2$

If they are divided by $10,17$ and $26$ respectively,

Then,

$\frac{x}{10}+\frac{x+1}{17}+\frac{x+2}{26}=10$

$\Rightarrow 442x+\left(260\right)(x+1)+\left(170\right)(x+2)=442\times 100$

$\Rightarrow 872x+600=442\times 100$

$\Rightarrow x=50$

So, the consecutive numbers are $50,51$ and $52$