Question

Find three consecutive numbers such that when they are divided by 2, 5 and 4 respectively, the sum of the result is 14.

• A. 12, 13, 14
• B. 14, 15, 16
• C. 13, 14, 15
• D. 15, 16, 17

Answer 1

The correct option is B 14, 15, 16

Let three consecutive numbers are $x$, $x+1$, $x+2$.

According to the given data,
$\frac{x}{2}+\frac{x+1}{5}+\frac{x+2}{4}=14$

By multiplying both sides by 20 [LCM of 2, 5 and 4], we get
$\Rightarrow 20\times (\frac{x}{2}+\frac{x+1}{5}+\frac{x+2}{4})=20\times 14$
$\Rightarrow 10x+4(x+1)+5(x+2)=280$
$\Rightarrow 10x+4x+4+5x+10=280$
$\Rightarrow 19x+14=280$
$\Rightarrow 19x=280-14$
$\Rightarrow 19x=266$
$\Rightarrow x=\frac{266}{19}$
$\Rightarrow x=14$

So, one of the numbers is 14 and other two numbers are $x+1=14+1=15$ and $x+2=14+2=16$.

$\therefore$ The three consecutive numbers are 14, 15 and 16.