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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?

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446

561

682

862

answer is D.

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Detailed Solution

Given, the sum of the digits

= 16

.
Let the hundredth's digit of the number be

x

.
Then unit's digit

= \frac{x}{4}

and tens digit

= \frac{3 x}{4}

.
According to the given condition,

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

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

\Rightarrow 2 x = 16

\Rightarrow x = 8

The tens digit

= \frac{3 x}{4} = \frac{3 \times 8}{4} = 6

.
The unit's digit,

= \frac{x}{4}

= \frac{8}{4}

= 2

Required number,

= 100 \times 8 + 10 \times 6 + 2

= 800 + 60 + 2

= 862

Hence, the correct option is 4.

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