Question

A two-digit number is such that, it exceeds the sum of the number formed by reversing the digits and sum of the digits by 4 . Also, the original number exceeds the reversed number by 18 . Find the product of the digits.

• A. 48
• B. 36
• C. 42
• D. 56

Answer 1

Answer: (A)

Let $x,y$ be the tens and units digits respectively.
Sum of the digits $=x+y$
Value of the number $=10x+y$
$10x+y=x+y+4+10y+x$
$8x-10y=4$ or $4x-5y=2$
Also given that,
$10x+y=10y+x+18$
$x-y=2$
Multiply Eq. (2) by 4 , we have,
$4x-4y=8$
Subtract Eq. (1) from Eq. (3), we get, $y=6$
Substitute $y=6$ in Eq. (2), we have $x=8$.
The product of the digits $=48$.