Question

The sum of the digits of a three-digit number is $16$. If the ten's digit of the number is $3$ times the unit's digit and the unit's digit is one-fourth of the hundredth digit then what is the number?

• A. $446$
• B. $561$
• C. $682$
• D. $862$

Answer 1

The correct option is D $862$

Let the hundredth's digit of the number be $x$

Then unit's digit $=\frac{x}{4}$

and ten's digit $=\frac{3x}{4}$

Given,

The sum of the digits is $16$

$\Rightarrow x+\frac{x}{4}+\frac{3x}{4}=16$

$\Rightarrow \frac{4x+x+3x}{4}=16$

$\Rightarrow 2x=16$

$\Rightarrow x=8$

ten's digit $=\frac{3x}{4}=\frac{3\times 8}{4}=6$

unit's digit $=\frac{x}{4}=\frac{8}{4}=2$

$\therefore$ Required number $=100\times 8+10\times 6+2$

$=800+60+2=862$

The required number is $862$