Averages · Topic 3 of 6

🔗 a, b, c Relationships

2 exam question types, fully solved

Here you are told the average of a pair or a triple of unknowns — say the average of and , and of and — and asked for one value or a difference. The trick is to stop thinking in averages and switch to sums.

Multiply by the count, then cancel the shared letter

Step 1 — average to sum. “Average of two is 50” means their sum is . Always multiply the average by how many numbers it covers (2 for a pair, 3 for a triple) before doing anything else.

Step 2 — subtract overlapping sums. When two groups share a member, subtracting their sums makes the shared letter vanish:

The 5-second shortcut. For two same-size groups, the difference of the unique members is twice the difference of the averages:

For bigger systems (three triple-averages), add all the equations: each letter shows up twice, so the grand total is half the combined sum, and you peel off one variable at a time.

📊Average Builderinteractive

avg = 5.4

Sum (S)

Count (N)

Average

5.4

Average = 27 ÷ 5 = 5.4

If and , then .

Q1The average of P and Q is 45; the average of Q and R is 38. Find P − R.

Q2The average of a, b, c is 20; the average of b, c, d is 25. Then d − a equals:

Q3The average of 4 numbers is 50. One is replaced by 70 and the average becomes 55. The replaced number was:

📚

Real exam questions — a, b, c Relationships

2 question types · 8 solved examples from real SSC papers

Turn every “average of two” into a sum by multiplying by 2, then add or subtract the sums to cancel shared letters.

How to solve this type

First rule: turn every “average of two” into a sum by multiplying by 2. The average of

x

and

y

being

50

means

x + y = 100

— work with the sums, never the raw averages.
When two pairs share a member (like

a+b

and

b+c

), subtract the sums to cancel the shared letter:

(b+c)-(a+b) = c - a

.
Handy shortcut: if two pairs of the same size differ in average by

d

, the unique members differ by

2d

. So if avg

(a,b)

and avg

(b,c)

differ by 9, then

a - c = 18

The average of x and y is 50. The average of y and z is 60. Find z − x.

A15B18C20D25

The average of three numbers a, b, c is 40. The average of a and b is 36. Find c.

A54B50C48D52

The average of A and B is 25, the average of B and C is 18, and C = 12. Find A.

A22B18C20D26

The average of S1 and S2 is 30 more than the average of S2 and S3. If S3 = 50, find S1.

A95B110C80D105