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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Question : By interchanging the digits of a two-digit number, we get a number that is four times the original number minus 24. If the unit's digit of the original number exceeds its ten's digit by 7, then the original number is:
Option 1: 29
Option 2: 36
Option 3: 58
Option 4: 18
Question : There is a number consisting of two digits, the digit in the unit place is twice that in the tens place and if 2 is subtracted from the sum of the digits, the difference is equal to $\frac{1}{6}$th of the number. The number is:
Option 1: 26
Option 2: 25
Option 3: 24
Option 4: 23
Question : The tens digit of a two-digit number is larger than the unit digit by 7. If we subtract 63 from the number, the new number obtained is a number formed by the interchange of the digits. Find the number.
Option 1: 81
Option 2: 18
Option 3: 62
Option 4: 26
Question : The product of the digits of a 2-digit number is 12. If we add 36 to the number, the new number obtained is a number formed by the interchange of the digits. What is the number?
Option 1: 62
Option 2: 34
Option 3: 26
Option 4: 43
Question : The cube of the sum of two given numbers is 1728, while the product of the two given numbers is 32. Find the sum of the cubes of the two given numbers.
Option 1: 576
Option 2: 250
Option 3: 640
Option 4: 512
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