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A Two-Digit Number Exceeds the Sum of the Digits of that Number by 18. If the Digit at the Unit’s Place is Double the Digit in the Ten’s Place, What is the Number?

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Explanation

  • A two-digit number exceeds the sum of the digits of that number by 18.
  • If the digit at the unit’s place is double the digit in the ten’s place.
  • The number can be figure out in this way.

Let suppose the two-digit number is 10y + z and sum of digits will be y + z.

First Condition:

“10y + z” exceeds “y + z” by 18.

10y + z – 18 = y + z ________ (i)

By simplifying equation (i), we can easily figure out the value of y (y = 2).

Second Condition:

z is double of y

z = 2y ________ (ii)

By placing the value of y in equation (ii);  we can figure out the value of z (z = 4) and number [10y + z = 10(2) + 4 = 20 + 4 = 24]

To Find

Number = ?

Solution

Let suppose

Let suppose the two-digit number is 10y + z

According to the first given condition

10y + z – 18 = y + z

10y – 18 = y

10y – y = 18

9y = 18

y = 18/9

y = 2

According to second given condition

z = 2y

z = 2(2)

z = 4

Number = 10y + z

Number = 10(2) + 4

Number = 20 + 4

Number = 24 answer

Conclusion

A two-digit number exceeds the sum of the digits of that number by 18. If the digit at the unit’s place is double the digit in the ten’s place, the number will be 24.

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