Question

In a family of a husband, wife and a daughter, the sum of the husband's age, twice the wife's age and thrice the daughters age is 85; while the sum of twice the husband's age, 4 times the wife's age and 6 times the daughter's age is 170. It is also given that the sum of 5 times the husband's age, ten times the wife's age and 15 times the daughter's age equals 450. The number of possible solutions, in terms of the ages of the husband, wife and the daughter, to this problem is:

• A. 1
• B. 2
• C. Infinitely many
• D. None of the above

Answer 1

Let the husband's age be x
Let the wife's age be y
Let the daughter's age be x
According to question,
x + 2y + 3z = 85 ......... (1)
2x + 4y + 6z = 170 ......... (2)
5x + 10y + 15z = 450 ......... (3)
From Equation (2), x + 2y + 3z = 85
From Equation (3), x + 2y + 3z = 90
From Equation (1), x + 2y + 3z = 85
Hence, the above system of equation will give no solution.