Question

If two consecutive numbers are divided by 3 and 2 respectively, then the difference between the second quotient and the first quotient is 4. Find the consecutive numbers.

• A. 20, 21
• B. 21, 22
• C. 22, 23
• D. 23, 24

Answer 1

The correct option is B 21, 22

Let the consecutive numbers be $x$ and $x+1$.
According to the question,
$\frac{x+1}{2}-\frac{x}{3}=4\Rightarrow \frac{3(x+1)-2x}{6}=4\Rightarrow \frac{x+3}{6}=4\Rightarrow x+3=4\times 6\Rightarrow x=24-3\Rightarrow x=21$

So, the consecutive numbers are 21 and $x+1=21+1=22$.