Question

The sum of two digit number and the numerator obtained by reversing the order of it's digits is 165.if the digits differ by 3,find the number.identify solution will exist or not

Answer 1

Correct Question :

The sum of 2 digit number and the number obtained by reversing the order of the digit is 165. If the digit differ by 3, find the number , when ten's digit is bigger than the unit 's digit.

Given :

The number is two digit - 10x + y (assume)

sum of the number and it's reverse = 165

difference between digits = 3

★ To find :

the original number

★ Solution :

(10x + y) + (10y+x) = 165

11y + 11x = 165

11(x+y) = 165

$x+y = \frac{\cancel{165}}{\cancel{11}} \\ \\ \\ x+y = 15....(1)$

x-y = 3....(2)

(1)+(2)

x+y +x - y = 15+3

2x = 18

$x = \frac{18}{2} \\ \\ \\ x = 9 \\ \\ \\ x+y = 15 \\ \\ \\ 9+y = 15 \\ \\ \\ y = 15 - 9 = 6$

→ x = 9 , y = 6.

→ Therefore , the original number = 96 .