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. $24$
• B. $30$
• C. $36$
• D. $48$

Answer 1

The correct option is D $48$

Let the two digit number be $10x+y$, where $x$ and $y$ are the digits at tens and ones place respectively.
Then the number with digits reversed is $10y+x$
Given, $10x+y-(10y+x+x+y)=4$
$\Rightarrow 8x-10y=4$
$\Rightarrow 4x-5y=2$ ....(1)
Also, $10x+y-(10y+x)=18$
$\Rightarrow 9x-9y=18$
$\Rightarrow x-y=2$ ....(2)
Solving equations (1) and (2), we get $x=8,y=6$
So, product of their digits $=8\times 6=48$.