Question 60

Father’s age and daughter's age add upto 55. Daughter’s age is reverse of her father’s and difference in their ages is more than 10. How old is the daughter?

Solution

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Let the father's age be 10x+y and the daughter's age be 10y+x

Difference between their ages is more than 10 years. So the eqn is:

(10x+y)-(10y+x)>10

=> 9(x-y)>10

=> (x-y)>1.11    ...(1)

Also sum of their ages is 55.

(10x+y)+(10y+x)=55

=>11(x+y)=55

=> x+y = 5    ...(2)

Solving (1) and (2) together, we get x=4 and y=1

So, daughter's age is 14.

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