1. Tardigrade
  2. Question
  3. Mathematics
  4. 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.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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.

Pair of Linear Equations in Two Variables

Solution:

Let $x, y$ be the tens and units digits respectively.
Sum of the digits $=x+y$
Value of the number $=10 x+y$
$10 x+y=x+y+4+10 y+x$
$8 x-10 y=4$ or $4 x-5 y=2$
Also given that,
$10 x+y=10 y+x+18$
$x-y=2$
Multiply Eq. (2) by 4 , we have,
$4 x-4 y=8$
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 $=48$.