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1. 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 ?

A. 42

B. 52

C. 62

D. 72

Solution:

Let the ten's digit be x and the unit's digit be y
Then, number = 10x + y

\begin{aligned} ∴ 10 x + y = 7 (x + y) \\ \Leftrightarrow 3 x = 6 y \\ \Leftrightarrow x = 2 y \end{aligned}

Number formed by reversing the digits = 10y + x

\begin{aligned} ∴ (10 x + y) - (10 y + x) = 18 \\ \Leftrightarrow 9 x - 9 y = 18 \\ \Leftrightarrow x - y = 2 \\ \Leftrightarrow 2 y - y = 2 \\ \Leftrightarrow y = 2 \\ So, x = 2 y = 4 \end{aligned}

Hence,
∴ Required number
= 10x + y
= 40 + 2
= 42

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