Question

A number consists of two digits. The digit in the tens place exceeds the digit in the units place by $4$. The sum of the digits is $\frac{1}{7}$ of the number. The number is

• A. $27$
• B. $72$
• C. $48$
• D. $84$

Answer 1

The correct option is D $84$

Let the digit in the units place $=x$
Let the digit in the tens place $=x+4$
$\therefore$ The number is $10(x+4)+x=10x+40+x=11x+40$
Sum of the digits $=x+x+4=2x+4$
Given, $2x+4=\frac{1}{7}(11x+40)$
$\Rightarrow 14x+28=11x+40$

$\Rightarrow 3x=12$

$\Rightarrow x=4$
$\therefore$ the number is $11\times 4+40=44+40=84$.