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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 is in the Unit’s Place is 3 More than the Digit in the Ten’s place. What is the Number?

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Explanation

  • The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.
  • If the digit is in the unit’s place is 3 more than the digit in the ten’s place then the required number can be calculate as:

Let the unit digit is z and ten’s digit is y. So, number becomes “10y + z” and ratio between a two-digit number (10y + z) and the sum of the digits (y + z) of that number is 4 : 1.

10y + z : y + z = 4 : 1 ________ (i)

Simplification of equation (i) gives

2y = z ________ (ii)

The second condition of the question says

z – 3 = y ________ (iii)

Solving (ii) and (iii) simultaneously we can easily figure out the required number.

To Find

Number = ?

Solution

Let Suppose

Unit digit = z

Ten’s digit = y

Number = 10y + z

According to the first condition of the question

10y + z : y + z = 4 : 1

10y + z = 4 (y + z)

10y + z = 4y + 4z

10y – 4y = 4z – z

6y = 3z

2y = z ________ (i)

According to the second condition of the question

z – 3 = y putting in equation (i)

2 (z – 3) = z

2z – 6 = z

z = 6 and y = 3

Number = 10y + z = 30 + 6 = 36 answer

Conclusion

The ratio between a two-digit number and the sum of the digits of that number is 4:1. The number would be 36 if the digit is in the unit’s place is 3 more than the digit in the ten’s place.

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