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Question

X is a two – digit number, if it is known that its unit’s digit exceeds its ten’s digit by 2 and that the product of the given number and the sum of its digits is equal to 144. Then the number is:


  1. 24

  2. 26

  3. 42

  4. 46

  5. 29


Solution

The correct option is A

24


{ Let the ten's digits be x. Then, unit's digit = x+2

Number = 10x+(x+2)=11x+2;Sumofdigits=x+(x+2)=2x+2. (11x+2)(2x+2)=14422x2+26x140=011x2+13x70=0 (x2)(11x+85)=0x=2. Hence, required number = 11x + 2 = 24

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