Husband & wife have a combined age of 91. If husband is now twice as old as his wife was when he was as old as she is...

Question

A husband and wife have a combined age of 91. If husband is now twice as old as his wife was when he was as old as she is now.
How old are they now?

Answer 1

suppose current ages of husband and wife are x and y resp.
so,
x+y=91...........(i)
difference of there ages= y-x

now when husband's age was as the wife's age is now, i.e, y
then wife's age would be = y+age difference
= y+ (y-x)
=2y- x
now, according to problem,
x=2*(2y - x)
x=4y - 2x
3x - 4y=0
replacing x=91-y from (i)... we get
3*(91 - y) - 4y=0
273 - 3y - 4y =0
or,
7y = 273
y = 39
from (i), x = 52

So, husband's age = 52 and wife's age = 39.

Answer 2

This problem should be resolved by trial and error.
1st scenario.
Husband is 50 years old and Wife is 91 - 50 = 41 years old
When husband was 41 years old , she was 41 - 9 = 32 years old Ratio : 41/ 32 = 1,28
2nd scenario
Husband is 55 years old and Wife is 91 - 55 = 36 years old
When husband was 36 years old, she was 36 - (55-36) = 17 years old Ratio : 36/ 17 = 2.11
3rd scenario
Husband is 54 years old and Wife is 91 - 54 = 37 years old
When husband was 37 years old , she was 37- (54-37) = 20 Ratio ; 37/20 = 1,85
Age of husband is between 54 - 55 , and wife between 36 - 37
Solution
Husband is 54,6 years old and wife is 36,4 years old
When husband is 36,4 years ols, she was 36,4 - (54,6 - 36,4 ) = 18,2 Ratio = 36,4/18,2 = 2

Answer 3

She age is 30 years and 4 months
He age is 60 years 8 months

From
Maneesh kumar