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.

• A. 24
• B. 25
• C. 26
• D. 27

Answer 1

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)

$\left(i\right)\Rightarrow 10X+Y=4X+4Y$
$\Rightarrow 6X=3Y$
$\Rightarrow Y=2X---\left(iii\right)$
$\left(ii\right)\Rightarrow 9X+18=9Y$

$\Rightarrow X+2=Y---\left(iv\right)$
Substituting (iii) in (iv), we get:
X + 2 = 2X
$\Rightarrow$ X = 2
Thus, (iii) $\Rightarrow$ Y = 4
Hence, the required number is 24.