In a two digit number, if it is known that its units 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	Pick:
A) 42
B) 46
C) 22
D) 24
E) None
Sol.   Let the ten's digit be x.   Then, units digit = x + 2.   Number = 10x + (x+2) = 11x + 2;   Sum of digits = x + (x+2) = 2x +2.   ∴ (11x +2)(2x+2) + ( +2)= 
<gadget id="calculator">+ ( +2)</gadget>
<output>2</output>
2x +2.   ∴ (11x +2)(2x+2)= 144   ⇔ 22x2 + 26x - 140 = 0   ⇔ 11x2 + 13x - 70 = 0   ⇔ (x - 2)(11x+35) = 0 ⇔ x =2.   Hence, required number = 11x + 2 = 24.   Answer 24
<result>D</result>
In a two digit number, if it is known that its units 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