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:

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Solution

The correct option is A
24

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

Number = $10 x + (x + 2) = 11 x + 2; S u m o f d i g i t s = x + (x + 2) = 2 x + 2.$ $∴ (11 x + 2) (2 x + 2) = 144 \Leftrightarrow 22 x^{2} + 26 x - 140 = 0 \Leftrightarrow 11 x^{2} + 13 x - 70 = 0$ $\Leftrightarrow (x - 2) (11 x + 85) = 0 \Leftrightarrow x = 2.$ Hence, required number = 11x + 2 = 24

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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:

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)=144⇔22x2+26x−140=0⇔11x2+13x−70=0 ⇔(x−2)(11x+85)=0⇔x=2. Hence, required number = 11x + 2 = 24