Question

the age of man is same as his cousin's age with digit reversed. the man is 9 years old than his cousin,if the sum of thier age is 99 years then how old is the man
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Answer 1

Answer:

Let the man age be 10x+y.

It is given that the age of man is same as his wife's age with the digits reversed, so wife's age would be 10y+x

Now, sum of the ages given is 99 which means that:

10x+y+10y+x=99

⇒11x+11y=99

⇒11(x+y)=99

⇒x+y=  99 /11

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⇒x+y=9   (1)

Also, the man is 9 years older than his wife, therefore, man age = wife age+9 that is:

10x+y=10y+x+9

⇒10x−x+y−10y=9

⇒9x−9y=9

⇒9(x−y)=9

⇒x−y=  9/9

⇒x−y=1.....(2)

Adding equations (1) and (2), we get

(x+y)+(x−y)=9+1

⇒2x=10

⇒x=  10/2

⇒x=5

Substitute x=5 in equation (1) as follows:

5+y=9

⇒y=9−5=4

Therefore, the age of man with x=5 and y=4 is:

10x+y=(10×5)+4=50+4=54

Hence, the man is 54 years old.

Step-by-step explanation: