Question

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​

Answer 1

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