Question

A two - digit number is 7 times the sum of its digits.The number formed by reversing the digits is 18 less than the original number.Find the number.

• A. 25
• B. 43
• C. 24
• D. 42

Answer 1

The correct option is D 42

Let the two-digit number be 'xy'
So, the actual value of the number is 10x + y.
When the digits are reversed
Then, the actual value of the number becomes 10y + x.
$\therefore$ from the given condition,
10x + y = 7 (x+y) - - - (1)
10y + x = (10x + y) - 18 - - - (2)
From (1), we get:
10x - 7x = 7y - y
$\Rightarrow$ 3x = 6y
$\Rightarrow$ x = 2y
Putting x = 2y in (2), we get :
10y + 2y = 20y + y - 18
$\Rightarrow$ 12y = 21y - 18
$\Rightarrow$ 9y = 18
$\Rightarrow$ y = 2
So, x = 2y = 2 $\times$ 2 = 4
$\therefore$ The required number is 42.