A two-digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than the original number. What is the number ?

Answer: Option A

Let the ten's digit be x and the unit's digit be y
Then, number = 10x + y
$$\begin{array}{rl}& \therefore 10x+y=7\left(x+y\right)\\ & \iff 3x=6y\\ & \iff x=2y\end{array}$$
Number formed by reversing the digits = 10y + x
$$\begin{array}{rl}& \therefore \left(10x+y\right)-\left(10y+x\right)=18\\ & \iff 9x-9y=18\\ & \iff x-y=2\\ & \iff 2y-y=2\\ & \iff y=2\\ & \text{So, }x=2y=4\end{array}$$
Hence,
∴ Required number
= 10x + y
= 40 + 2
= 42