Lessons

General Aptitude
27.1 Problems on Numbers - General Questions

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Q.

In a two-digit, 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:

View Answer

Correct choice: A

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

⇒ 22x2 + 26x - 140 = 0

⇒ 11x2 + 13x - 70 = 0

⇒ (x - 2)(11x + 35) = 0

x = 2.

Hence, required number = 11x + 2 = 24.

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