Difficulty: Easy
Correct Answer: 70 years
Explanation:
Introduction / Context:
This age problem is simpler and primarily checks whether you can recognise how sums of ages change over time. When both people age by the same amount, the sum of their ages increases in a straightforward way.
Given Data / Assumptions:
Concept / Approach:
While we can find the individual ages of A and B, there is a simpler method. After 5 years, A s age increases by 5 and B s age also increases by 5. So the sum of their ages increases by 5 + 5 = 10. Therefore, the new sum is simply 60 + 10. We can still compute their specific ages to check consistency.
Step-by-Step Solution:
Let B s present age = x.
Then A s present age = 2x.
Given that A + B = 60.
So 2x + x = 60.
3x = 60, hence x = 20.
Therefore, B is 20 years old and A is 40 years old.
After 5 years, A s age = 40 + 5 = 45.
After 5 years, B s age = 20 + 5 = 25.
Sum after 5 years = 45 + 25 = 70 years.
Alternatively, we can simply add 10 to the original sum of 60 to get 70.
Verification / Alternative check:
From the computed ages, the present sum is 40 + 20 = 60, and after 5 years the sum is 70. This matches the logical shortcut that adding 5 years to both people adds 10 years to the total, confirming that 70 is correct.
Why Other Options Are Wrong:
Option 60 would be the present sum only and ignores the passage of time. Options 65 and 75 correspond to adding 5 or 15 years total, which would require asymmetric changes in ages or a different time interval.
Common Pitfalls:
Some learners mistakenly think that because A is twice as old as B, the change in their sum over time is more complicated. In fact, regardless of the ratio, if both individuals age by the same number of years, the total increase in the sum is just two times that number.
Final Answer:
The sum of their ages 5 years from now will be 70 years.
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