Averages — The Total-First Method (Matric Level)
Syllabus topic: Percentages, Ratio and Proportion, Averages
In the SSC GD paper, average questions are scoring because they need one idea only: average × count = total. Every standard question — a new member joining, a member leaving, a wrong value corrected — is solved by rebuilding the total, never by averaging the averages.
The one formula and its reverse
Average = (sum of values) ÷ (number of values). The exam more often gives you the average and asks for a missing value, so turn the formula around: sum = average × count. If the average age of 10 students is 15 years, their total age is 150 years — write the total down first, every time.
When a person joins or leaves, compute both totals and subtract. If an 11th student joins and the average rises to 16, the new total is 176, so the newcomer is 176 − 150 = 26 years old. The same subtraction handles replacements: if a member is replaced and the average changes, the difference in totals belongs entirely to the swap.
- Total = Average × Count — write the total first
- New member's value = new total − old total
- Corrected average: fix the total (add back the wrong value, subtract the right one), then divide
- Average speed for equal distances = 2xy/(x + y), not (x + y)/2
Shortcuts worth memorising
The average of the first n natural numbers is (n + 1)/2; of the first n even numbers is n + 1; of the first n odd numbers is n. Consecutive numbers in any evenly spaced list average to the middle term — if the list has an even count, the average is the mean of the two middle terms. These four facts answer a steady share of GD average questions without any calculation.
Key points to remember
- Always convert the average into a total before doing anything else.
- Joining, leaving and replacement questions are total-subtraction questions.
- Never average two averages unless both groups have the same count.
- For equal distances, average speed = 2xy/(x + y).
Topic from the official SSC GD Constable syllabus (Elementary Mathematics) as published in NaukriHelp's SSC GD exam guide. Note written by NaukriHelp; standard mathematics references used for the subject only.