In a family, the combined age of husband, wife and a son is 90 years. The husband is the oldest. The difference in the ages of the husband and wife is 1/3rd the age of their son. After 10 years, the age of the son would be half the age of his father. What is the present age of his mother (in years)?

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Accepted Answer

Let the present ages of the husband, wife, and son be H, W, and S respectively.

Given:
1. H + W + S = 90
2. H is the oldest.
3. The difference between husband's and wife's ages is 1/3rd the age of the son:
   H - W = (1/3) * S
4. After 10 years, son's age will be half the father's age:
   S + 10 = (1/2)(H + 10)

From equation (4):
2(S + 10) = H + 10
2S + 20 = H + 10
H = 2S + 10

From equation (3):
H - W = S/3
Substitute H from above:
(2S + 10) - W = S/3
W = (2S + 10) - S/3 = (6S/3 + 10) - S/3 = (5S/3) + 10

Now use equation (1):
H + W + S = 90
(2S + 10) + ((5S/3) + 10) + S = 90
Combine terms:
2S + 10 + 5S/3 + 10 + S = 90
(2S + S) + 5S/3 + 20 = 90
3S + 5S/3 + 20 = 90
Convert 3S to fraction with denominator 3:
(9S/3) + (5S/3) + 20 = 90
(14S/3) + 20 = 90
14S/3 = 70
14S = 210
S = 15

Now find H and W:
H = 2S + 10 = 2*15 + 10 = 40
W = (5S/3) + 10 = (5*15/3) + 10 = 25 + 10 = 35

Therefore, the present age of the mother (wife) is 35 years.

Check the options: 35 is option 3.

Re-checking the son's age after 10 years:
Son's age after 10 years = 15 + 10 = 25
Father's age after 10 years = 40 + 10 = 50
Son's age is half of father's age: 25 = 50/2, which is correct.

Hence, the correct answer is 35 years.

Answer

Answer

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