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In a family, the sum of the ages of a father and son is 60 years. 5 years from now, the difference in their ages will be 24 years. Find the ratio of the son's age to the father's age.
1:3
2:3
1:2
3:7
3
Since the age difference between two people is constant, the difference remains 24 years forever. Just solve the simple system: F+S=60 and FтИТS=24.
Sum of father's and son's ages is 60. The difference in their ages 5 years from now is 24.
F+S=60,FтИТS=24
Since the age difference between two people is constant, the difference remains 24 years forever. Just solve the simple system: F+S=60 and FтИТS=24.
Students often incorrectly calculate the difference in ages after 5 years, forgetting that the age gap between a father and son is invariant over time.
Define the variables and constants
Let F be the father's age and S be the son's age. We are given the sum as F+S=60.
F+S=60
Establish the age difference
Since the age difference remains constant regardless of the passage of time, the difference is FтИТS=24.
FтИТS=24
Solve for F and S
Adding the two equations: 2F=84, which implies F=42. Substituting F into the first equation: 42+S=60, so S=18.
F=42,S=18
Calculate the ratio
The ratio of the son's age to the father's age is FSтАЛ=4218тАЛ. Dividing both by their HCF 6, we get 73тАЛ. Wait, checking calculation: 60тИТ24=36,36/2=18 (son). 18+24=42 (father). 18/42=3/7. Let me re-read the prompt. Ah, the provided answer A is 1:3. Let's re-verify. If S=15,F=45, sum is 60, difference is 30. That is not 24. Let's re-calculate S+F=60,FтИТS=24. 2F=84,F=42,S=18. The ratio is 18:42=3:7. There might be a typo in the provided option A.
4218тАЛ=73тАЛ
D is correct because the calculated ratio of son to father is 3:7 based on the system of equations F+S=60 and FтИТS=24.
Age difference problems are essentially constant difference problems, similar to ratio distribution problems in Mixtures and Allegations.
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