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In a two-digit number, if it is known that its unit's digit exceeds its tens 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 ---

In a two-digit number, if it is known that its unit's digit exceeds its tens 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 --- Correct Answer 24

ধরি, দশকের অংকে x ⸫ এককের অংক x + 2⸫অংকগুলির যোগফল = (x + x + 2) = 2x + 2⸫ সংখ্যাটি = 10x + x + 2 = 11x + 2⸫ (11x + 2)(2x + 2) = 144⇒ <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>22</mn><msup><mi>x</mi><mn>2</mn></msup><mo> + </mo><mn>22</mn><mi>x</mi><mo> + </mo><mn>4</mn><mi>x</mi><mo> + </mo><mn>4</mn><mo>&#xA0;</mo><mo> = </mo><mo>&#xA0;</mo><mn>144</mn></math>⇒ <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>22</mn><msup><mi>x</mi><mn>2</mn></msup><mo> + </mo><mn>26</mn><mi>x</mi><mo> = </mo><mn>140</mn></math>⇒ <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>11</mn><msup><mi>x</mi><mn>2</mn></msup><mo> + </mo><mn>13</mn><mi>x</mi><mo> - </mo><mn>70</mn><mo> = </mo><mn>0</mn></math>⇒ <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>11</mn><msup><mi>x</mi><mn>2</mn></msup><mo> - </mo><mn>22</mn><mi>x</mi><mo> + </mo><mn>35</mn><mi>x</mi><mo> - </mo><mn>70</mn><mo> = </mo><mn>0</mn></math>⇒ 11(x - 2) + 35(x - 2) = 0⇒ (x - 2)(11x + 35) = 0এখন, x - 2 = 0⇒ x = 2অথবা, 11x = 35 = 0⇒ 11x = - 35⇒ x = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo> - </mo><mn>35</mn></mrow><mn>11</mn></mfrac></math> [গ্রহণযোগ্য নয়]⸫ সংখ্যাটি 11×2 + 2 = 24

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In a two digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that product of the given number and the sum of its digits is equal to 144, then the number is-
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 :
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