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A father's age is 2 years more than 4 times the age of his son. His age is also 2 years more than 5 times the age of his daughter. The average age of the father, the son and the daughter is 20 years. What is the age of the daughter?

Explanation

Let the ages of the father, son, and daughter be F, S, and D respectively.

From the given conditions:
1. F = 4S + 2 → S = (F - 2)/4
2. F = 5D + 2 → D = (F - 2)/5
3. The average age is 20: (F + S + D)/3 = 20 → F + S + D = 60

Substitute S and D in the sum equation:
F + (F - 2)/4 + (F - 2)/5 = 60

Multiplying the entire equation by 20 (LCM of 4 and 5) to clear denominators:
20F + 5(F - 2) + 4(F - 2) = 1200
20F + 5F - 10 + 4F - 8 = 1200
29F - 18 = 1200
29F = 1218
F = 1218/29 = 42

Now, calculate the daughter's age:
D = (42 - 2)/5 = 40/5 = 8 years.

Change set

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A father's age is 2 years more than 4 times the age of his son. His age is also 2 years more than 5 times the age of his daughter. The average age of the father, the son and the daughter is 20 years. What is the age of the daughter?

Explanation

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