Question : The ratio of a two-digit number and the sum of the digits of that number is 4 : 1. If the digit at the unit's place is 3 more than the digit at the ten's place, then the number is:
Option 1: $47$
Option 2: $69$
Option 3: $36$
Option 4: $25$
Correct Answer: $36$
Solution :
Let us assume that the digits of the number are $x$ and $y$ with $x$ in the ten's place.
The number is $10x+y$.
The digit in the unit's place is 3 more than the digit in the ten's place, i.e. $y=x+3$ ...(1)
The ratio between the two-digit number and the sum of the digits of that number is $4 : 1$.
$(10x+y):(x+y) = 4:1$
or, $10x+y = 4x+4y$
or, $y = 2x$
Substituting in (1), we get $2x = x+3$
$x = 3, y = 6$
The number is $36$.
Hence, the correct answer is $36$.
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