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The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's place is 3 more than the digit in the ten's place, then the number is ?

The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's place is 3 more than the digit in the ten's place, then the number is ? Correct Answer 36

Let the ten's digit be x
Then, units digit = x + 3
Number = 10x + (x + 3)
              = 11x + 3
Sum of digits = x + (x + 3)
                      = 2x + 3
$$\eqalign{ & \therefore \frac{{11x + 3}}{{2x + 3}} = \frac{4}{1} \cr & \Leftrightarrow 11x + 3 = 8x + 12 \cr & \Leftrightarrow 3x = 9 \cr & \Leftrightarrow x = 3 \cr} $$
Hence, Required number
= 11x + 3
= 11 × 3 + 3
= 36

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