Question

The tens digit of a two digit number is twice of its units digit, on reversing the digits the number formed is 27 less than the original number. Find the original number.

Answer 1

Given:

• The tens digit of a two digit number is twice of its units digit
• On reversing the digits, the number formed is 27 less than the original number

To find: the original number

Solution:

Let the digits in units and tens places be x and y.

Then the number is y + 10x

When the digits are reversed, the number becomes x + 10y

By the given conditions,

• y = 2x ... ...(i)
• y + 10x = x + 10y - 27
• or, 2x + 10x = x + 10 * 2x - 27 [using (i)]
• or, 12x = x + 20x - 27
• or, 21x - 12x = 27
• or, 9x = 27
• or, x = 3

Putting x = 3 in (i), we get

• y = 2 * 3
• or, y = 6

Thus the original number is

• y + 10x = 6 + 10 * 3 = 6 + 30 = 36

Answer: the original number is 36.

Answer 2

Answer:

the original number is 36