The total of the present ages of Ashok, Akbar and Anil is 65 years. What was the total of their ages six years ago?

Introduction / Context:
This question belongs to the basic level of age problems where the total present age of a group is known and we are asked to find the total at some time in the past. It tests whether you understand that each person age changes by the same amount over a fixed time period, and hence the total change in the sum of ages is simply the number of people multiplied by that time interval.

Given Data / Assumptions:

• The total of the present ages of Ashok, Akbar and Anil is 65 years.
• We have to find the total of their ages six years ago.
• There are exactly three people in the group.
• All ages are measured in years.

Concept / Approach:
If there are n people in a group, then going back t years means each person age is reduced by t years. Therefore, the sum of their ages t years ago is the present sum minus n * t. This applies regardless of how old each individual is, as long as the number of people remains the same. Here, n is 3 and t is 6, so we can compute the total six years ago directly from the given total present age.

Step-by-Step Solution:
Step 1: The present total age of Ashok, Akbar and Anil is given as 65 years. Step 2: Six years ago, each of the three people was 6 years younger than they are now. Step 3: The total decrease in the sum of ages over 6 years for 3 people is 3 * 6 = 18 years. Step 4: Therefore, the sum of their ages six years ago was 65 - 18 years. Step 5: Compute the difference: 65 - 18 = 47 years. Step 6: So, the total of their ages six years ago was 47 years.

Verification / Alternative check:
As an alternative check, imagine any three ages that now add up to 65 years, for example 20, 22 and 23. Six years ago these would have been 14, 16 and 17, and their sum would be 47. This shows that regardless of the individual distribution, the total decreases by 18 years, confirming the formula and result. The key is that only the total matters for this question.

Why Other Options Are Wrong:
Option A (59 years) represents a decrease of only 6 years, which would correspond to only one person getting younger, not three people, so it is incorrect.
Option B (43 years) would imply a decrease of 22 years, which does not match 3 * 6 and therefore is not possible for three people going back six years.
Option C (57 years) corresponds to a decrease of 8 years, again not equal to 18 years, so it is also wrong.

Common Pitfalls:
Many learners mistakenly subtract 6 only once from the total instead of six times for each of the three people. Others attempt to guess individual ages even though they are not needed. Remember that when the number of people is fixed, total change over t years for n people is n * t, which simplifies such problems greatly.

Final Answer:
The total of their ages six years ago was 47 years.