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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.
  1. 24
  2. 25
  3. 26
  4. 27


Solution

The correct option is A 24
Let 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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