A woman says, “If you reverse my own
age, the figures represent my husband's
age. He is, of course, senior to me and the
difference between our ages is one-eleventh
of their sum.” The woman's age is
Answers
Answer:
the husbands age is 54
the womans age is 45
Step-by-step explanation:
let us assume the womans age be 10x+y (2 digit number)
=> her husbands age = 10y+x (given)
also, 10y+x - (10x+y) = (10x+y+10y+x)/11
=> 11(10y-10x+x-y) = 11x+11y
=> 11(9y-9x) = 11x+11y
=> 99(y-x) = 11(x+y)
=> 9(y-x) = (x+y)
=> 9y-y-9x-x=0
=> 8y-10x = 0
=> 4y-5x = 0
=> 5x = 4y => x = 4y/5 and y = 5x/4
as x and y are natural no.s,
we assume x =4 to make y a natural number in y = 5x/4
=> y = (5*4)/4 = 20/4 = 5
=> x = (4*5)/5 = 20/5 = 4
=> the husbands age is 10y+x = 10(5) + 4 = 50+4 = 54
=> the womans age is 10x+y = 10(4)+5 = 40+5 = 45
verification:
1) when the womans age, 45 is reversed we get 54, which is the husbands age.
2) sum = 45+54 = 99 and diff = 54-45 = 9
=> diff = 99/11 = sum/11
ie, diff = one eleventh of the sum