Question

The sum of the digits of a two digit number is 9. If the digits are reversed the new number decreased by 9 is equal to 4 times the original number.Find the original number ​

Answer 1

Answer:

• The original number is 18.

Given:

• The sum of the digits of a two digit number is 9.

• If the digits are reversed then new number is decreased by 9 is equal to 4 times the original number.

To find:

• The original number.

Solution:

Let the unit place of the number be x and it's unit place be y.

According to the first condition.

=> x + y = 9

=> x = 9 - y ...(1)

Here,

• Original number = 10x + y

• Number with reversed digits = 10y + x

According to the second condition.

=> 10y + x - 9 = 4 (10x + y)

=> 10y + x - 9 = 40x + 4y

=> -39x + 6y = 9 ...(2)

Substituting eq(1) in eq(2), we get

=> -39 (9 - y) + 6y = 9

=> -351 + 39y + 6y = 9

=> 45y = 360

=> y = 8

Substituting y = 8 in equation (1), we get

=> x = 9 - 8

=> x = 1

Original number = 10x + y = 10(1) + 8 = 18

Therefore, the original number is 18.