Question

The sum of a two digit number formed by interchanging it's digits is 88.If the sum of sum and difference of the digits of the number is 8, what is the number?

Give the correct Proof.

Answer 1

Answer:

given number = 44

Step-by-step explanation:

let the two digit number =10x + y

A.T.Q

10x + y + 10y + x = 88

11x + 11y = 88

divide by 11

x + y = 8 -------(1)

(x + y) + (x - y) = 8

x + y + x - y = 8

2x = 8

x = 8/2

x = 4

put x in eq 1

x + y = 8

4 + y = 8

y = 8 - 4

y = 4

then given number = 10x + y

10 × 4 + 4

= 44 + 4

= 44

verification

put x and y in eq 1

x + y = 8

4 + 4 = 8

8 = 8

LHS = RHS