Question

In a two-digit number, the digit at the units place is double the digit in the tens place. The number exceeds the sum of its digits by 18. Find the number.

Answer 1

We know that the digit at the units place is double the digit in the tens place.

So let’s consider the tens place as y

The digit at the unit place is 2y

So the equation is (10y + 2y) = 12y…………….. Equation (1)

From the question, the number exceeds the sum of its digits by 18

∴from the above condition, (y + 2y) + 18……….. Equation (2)

Combining equation 1 and 2 we get,

(y + 2y) + 18 = (10y + 2y)

3y + 18 =12y

18 = 12y -3y

18 = 9y

∴ y = 2

Hence, the digit tens place is 2

The digit unit place is 2y = 2(2) = 4

Substituting the value of y in equation 1 we get,

12y

12(2) = 24

∴ The required number is 24.