The sum of a two digit number and the number obtained by reversing the order of the digits is 165. When 9 is subtracted from the number the digits interchange their places find the number.
Answers
Let us assume, x and y are the two digits of a two-digit number.
Therefore, the two-digit number = 10x + y
And the reverse number = 10y + x
Given:
10x + y + 10y + x = 165
11x + 11y = 165
x + y = 15 ------------1
Also given:
10x + y – 9 = 10y + x
9x – 9y = 9
x – y = 1 -----------------2
Subtract equation 2 from equation 1
2x = 14
x = 7
Therefore, y = 15 – x = 15 – 7 = 8
Therefore, the Two-digit number = 10x + y = (10 * 7) + 8 = 78Answer: The original number is 87
Step-by-step explanation:
Let us assume, x and y are the two digits of a two-digit number.
Therefore, the two-digit number = 10x + y
And the reverse number = 10y + x
Given:
10x + y + 10y + x = 165
11x + 11y = 165
x + y = 15 ------------1
Also given:
10x + y – 9 = 10y + x
9x – 9y = 9
x – y = 1 -----------------2
Subtract equation 2 from equation 1
x+y=15
x-y=1
2y=14
y=7(The x's get cancelled out since x-x=0,so x=7 is wrong)
Upon substituting y=7 in 2
x-7=1
x=1+7
x=8
Therefore the original no is 10x+y
(10 x 8) + 7
=87