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 ?
6 years
12 years
10 years
8 years
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CISF-AC-EXE – 2023
According to the first statement: F = 4S + 2
According to the second statement: F = 5D + 2
According to the third statement: (F + S + D) / 3 = 20, which simplifies to F + S + D = 60.
From the first two equations, we can equate the expressions for F:
4S + 2 = 5D + 2
4S = 5D
S = 5D / 4
Now substitute the expressions for F and S in terms of D into the average age equation:
(5D + 2) + (5D / 4) + D = 60
Multiply the entire equation by 4 to eliminate the fraction:
4(5D + 2) + 5D + 4D = 240
20D + 8 + 5D + 4D = 240
(20 + 5 + 4)D + 8 = 240
29D + 8 = 240
29D = 240 – 8
29D = 232
D = 232 / 29
D = 8
The age of the daughter is 8 years.
– Use substitution to solve the system of equations.
Daughter’s age (D) = 8 years.
Father’s age (F) = 5D + 2 = 5(8) + 2 = 40 + 2 = 42 years.
Son’s age (S) = (F – 2) / 4 = (42 – 2) / 4 = 40 / 4 = 10 years.
Check the average: (F + S + D) / 3 = (42 + 10 + 8) / 3 = 60 / 3 = 20 years. This matches the given information.