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QThere is a two-digit number whose ratio to the sum of its digits is 4:1, and the digit in the unit's place is 3 more than the digit in the ten's place. Determine the value of this number.

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#4481Q ID
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  • A 16 ✔ ✖
  • B 35 ✔ ✖
  • C 36 ✔ ✖
  • D 40 ✔ ✖
Correct Answer: Option C

Explanation

Given:

The ratio between a two-digit number and the sum of the digits of that number is 4:1
The digit in the unit's place is 3 more than the digit in the ten's place
Let the digit in the ten's place be x.
Then the digit in the unit's place is x + 3 and the sum of the digits is 2x + 3. 
The two-digit number can be expressed as:

10x + (x + 3) = 11x + 3
The ratio of the number to the sum of its digits is given by:

(11x + 3) / (2x + 3) = 4/1
Solve for x:

3x = 9
x = 3
Therefore, the two-digit number is 11x + 3 = 11(3) + 3 = 36.

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