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A husband and wife have a combined age of 91. The husband is
now twice as old as his wife was when he was as old as she is
now. How old is wife?
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Answer Posted / yonas demissie hankarso
Let H be husband's current age,
W be wife's current age,
H' be husband's age years back,
W' be wife's age years back.
What's already given is
H + W = 91............eq1
H = 2W'..................eq2
H' = W....................eq3
But we know that current age difference and age difference years back is the same, therefore ;
H - W = H' - W'.........eq4
substituting eq2&eq3 into eq4, we have,
H - W = W- H/2
--> H + H/2 = W + W
--> 3/2H = 2W
--> H = 4/3W..........eq5
substituting eq5 into eq1 we have
4/3W + W = 91
--> 7/3 W = 91
--> W = 91×3/7
--> W= 39
from eq 1 we have H = 91- W
H = 91- 39 = 52
Therefore husband is 52 years of age while wife is 39 years of age.
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