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28
Q:

In 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 :

A) 12 B) 24
C) 36 D) 48

Answer:   B) 24



Explanation:

Let the ten's digit be x.

 

Then, unit's digit = x + 2.

 

Number = 10x + (x + 2) = 11x + 2

 

Sum of digits = x + (x + 2) = 2x + 2.

 

(11x + 2) (2x + 2) = 144

=> 22x^2+26x-140=0

 

=> (x - 2)(11x + 35) = 0

 

=> x = 2

 

Hence, Required Number = 11x + 2 = 24

Subject: Problems on Numbers
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