A two – digit number is 4 times the sum of its digits. The number obtained by interchanging the digits is greater by 9 than the original number. Find the original number. Ans. The original number is 12.
Answer: The original number is 12.
Let the tens digit be \(x\) and the units digit \(y\). The number is \(10x + y\).
Number is 4 times the sum of digits:
\[10x + y = 4(x + y) \Rightarrow 6x = 3y \Rightarrow y = 2x \quad\text{(1)}\]
Reversed number is 9 more:
\[(10y + x) - (10x + y) = 9 \Rightarrow 9(y - x) = 9 \Rightarrow y - x = 1 \quad\text{(2)}\]
From (1) and (2): \(2x - x = 1 \Rightarrow x = 1\), \(y = 2\).
Number = 12. Check: 4 × (1 + 2) = 12 and 21 − 12 = 9.
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