Question : In a two-digit number, its unit digit exceeds its tens digit by 2 and the product of the given number and the sum of its digits is equal to 460. The number is:
Option 1: 48
Option 2: 64
Option 3: 46
Option 4: 36
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Correct Answer: 46
Solution :
Given: In a two-digit number, its unit digit exceeds its tens digit by 2 and the product of the given number and the sum of its digits is equal to 460.
Let the number's unit digit be $y$ and its tens digit be $x$.
Then, the two digits number = $10x + y$.
Also, $y=x+2$
According to the question,
$(10x+y)\times (x+x+2)=460$
⇒ $(10x+y)\times (2x+2)=460$
By hit and trial, substitute the value of $x=4$ and $y=6$,
⇒ $(10\times 4+6)\times (2\times 4+2)=460$
⇒ $46\times 10=460$
The number = $10x+y=10\times 4 +6=46$.
Hence, the correct answer is 46.
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