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The current ages of A and B add up to 36 years. Four years ago, the age of A was three times than that of B. What is the current age of A?
25 years
20 years
30 years
35 years
25 years
To solve age-based problems, we define the ages as variables based on the given constraints. Given the total sum and a relative age relationship from the past, we set up a system of linear equations to isolate the variables.
To solve age-based problems, we define the ages as variables based on the given constraints. Given the total sum and a relative age relationship from the past, we set up a system of linear equations to isolate the variables.
Think of this like balancing a scale; if you shift time backward for one person, you must shift it equally for the other to maintain the correct historical comparison.
A+B=S тАФ Total sum of ages
(AтИТn)=k(BтИТn) тАФ Relation after n years at ratio k
Let the current age of A be A and B be B. The first condition is A+B=36. Four years ago, their ages were (AтИТ4) and (BтИТ4) respectively. According to the problem, (AтИТ4)=3(BтИТ4). Solving the system: A=36тИТB. Substituting this: (36тИТBтИТ4)=3(BтИТ4)тЯ╣32тИТB=3BтИТ12тЯ╣44=4BтЯ╣B=11. Therefore, A=36тИТ11=25.
Always identify the time reference (current vs past/future).
A decrease in time affects all individuals in the group equally.
Verify the sum in the final answer to ensure consistency.
Systematic approach reduces calculation errors.
Algebraic methods are universally applicable to all age problems.
Population demographics analysis
Predictive growth modeling
The age difference between two people remains constant over time.
Option B (20) implies B would be 16, 4 years ago, but 20-4=16 and 16-4=12; 16 is not 3 times 12.
A is correct тАФ The current age of A is 25 years, satisfying both the total sum and the ratio condition.
In competitive exams, always check the options by plugging them back into the 'past condition' equation to save time.
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