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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


Team Careers360 5th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

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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