Question

The age of a man is same as his wife, s age with the digits reversed then sum of their ages is 99 and the man is 9 years order than his wife how old is the man

Answer 1

Hi there !
Here's the answer:


•°•°•°•°•°<><><<><>><><>°•°•°•°•°

Let man's age = 10x+y
where x = tens digit of his age
and y =units digit of his age

Wife's age = 10y+x
(Digits are reversed)

Given,
(10x+y) + (10y+x) = 99
= 11x + 11y = 99
=> x + y = 9 ____(1)

Also given,
(10x+y) - (10y+x) = 9
( Man is 9 years older. Difference of their age = 9 )

=> 9x - 9y = 1
=> x - y = 1 ____(2)


Do (1) + (2)

x + y = 9
x - y = 1
---------------
2x = 10
=> x = 5

Sub x= 5 in (1)
=> 5 + y = 9
=> y = 9 - 5
=> y = 4

•°• x = 5 & y = 4


•°• Man's age = 10x+y = 54
& His wife's age = 10y+x = 45

•°•°•°•°•°<><><<><>><><>°•°•°•°•°


¢#£€®$

:)


Hope it helps

Answer 2

Here is your solution

Given that :-

The age of a man is same as his wife

age with the digits reversed then sum of their ages is 99 and the man is 9 years order than his wife


Let
The man age = 10x +y

wife age = 10y +x

sum of the ages = 99

10x+y +10y +x =99

11x +11y =99

x+y =9................................................ (1)

man age = wife age+9

10x +y = 10y +x+9
10x-x +y -10y =9
9x -9y =9


x-y =1 ...............................................(2)

Adding equation (1) and (2)

2x =10
x= 10/2
x= 5

putting the value of x=5 in equation (1)

y= 4

Hence,
man age =10x+y = 10*5 +4 =50+4 = 54✔

Age of wife = 45 years. ✔

Hope it helps you