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The age of a father is twice the sum of the ages of his 3 children. After 15 years, his age will be equal to the sum of the ages of his children. How old will the father be 15 years later?
75 years
90 years
95 years
85 years
75 years
Since the father's age increases by 15 years while the sum of 3 children's ages increases by 3*15=45 years, the father's age 15 years later is simply the value that balances this new equality, which leads to F=60 current age, so 60+15=75.
Let F be the father's current age and S be the sum of the ages of his 3 children. Equation 1: F = 2S. Equation 2: (F + 15) = S + (3 * 15).
F=2S, F+15=S+45
Since the father's age increases by 15 years while the sum of 3 children's ages increases by 3*15=45 years, the father's age 15 years later is simply the value that balances this new equality, which leads to F=60 current age, so 60+15=75.
A common mistake is adding 15 only once to the children's ages, forgetting that there are 3 children, so the total sum increases by 45, not 15.
Define variables
Let the father's current age be F and the sum of the ages of his 3 children be S.
F=2S
Formulate equation for 15 years later
After 15 years, the father's age will be F+15. Each of the 3 children will also age 15 years, so the new sum of their ages will be S+3├Ч15=S+45.
F+15=S+45
Substitute and solve
Substitute F=2S into the second equation: 2S+15=S+45. Solving for S, we get S=30.
2SтИТS=45тИТ15тЯ╣S=30
Find the father's future age
The father's current age is F=2S=2(30)=60. His age 15 years later will be 60+15=75.
60+15=75
A is correct because the father's current age is 60, and after 15 years, he will be 75.
This concept of 'sum of ages' is frequently tested in banking and railway exams; always remember to multiply the year difference by the number of people in the group.
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