Question

# A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.24252627

Solution

## The correct option is A 24Let the 2-digit number by XY, whose expanded form is 10X + Y. The number obtained by reversing its digits is YX, whose expanded form is 10Y + X. As per the data, 10X + Y = 4(X + Y) --- (i) and 10X + Y + 18 = 10Y + X --- (ii) (i)⇒10X+Y=4X+4Y ⇒6X=3Y ⇒Y=2X−−−(iii) (ii)⇒9X+18=9Y ⇒X+2=Y−−−(iv) Substituting (iii) in (iv), we get: X + 2 = 2X ⇒ X = 2 Thus, (iii) ⇒ Y = 4 Hence, the required number is 24.

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