## Average Related Problems

(Quantitative Reasoning)

The average of given set of numbers can be expressed as:

 A = Sum of the quantities of same kind Number of quantities of the same kind.

Important Points:

Sum of Quantities = Number of quantities × Average

Average is also called the Arithmetic Mean.

If all the given quantities have the same value, then the vaue itself is the average.

If each of the given quantities is increased/decreases by a constant N, then their average is also increased/decreased by N.

If each of the given quantities is multiplied by a constant N, then their average is also multiplied by N.

Solved Problems:

Q1: Fnd the average of first five even numbers.

Answer: A = (2 + 4 + 6 + 8 + 10)/5 = 30/5 = 6

Q2: If the average of p and q is 58 and the average of q and s is 64, what is the value of s-p?

Answer: (p + q)/2 = 58      ⇒ p + q = 116       ...(i)
(q + s)/2 = 64      ⇒ q + s = 128               ...(ii)

Subtract (i) from (ii),

q + s - p - q = 128 - 116

s - p = 12

Q3: The average weight of 10 men is increased by 1½ kg, when one of the men who weighs 68 kg is replaced by a new man. Find the weight of the new man.

Answer: Average increase in weight = 1½ kg
No. of men = 10
Total increase = 10 × 1½ = 15kg
Weight of new man = Weight of previous man + Total increase in weight
= 68 + 15 = 83kg.

Q4: The average of 10 numbers is 7. If each number is multiplied by 12, then the average of new set of numbers is ___?

Answer: 12 ×  7 = 84.
If each of the given quantities is multiplied by a constant N, then their average is also multiplied by N.

Q5: Of three numbers, the first is two times the second and the second is thrice the third. If the average of three numbers is 10, find the numbers.

Answer: Let 3rd no. = x
2nd number      = 3x
1st number      = 6x

Ratio of 1st : 2nd : 3rd = 6 : 3: 1

Sum of ratios = 6x + 3x + x = 10x
Average of three numbers = 10x/3 = 10

⇒ x = 3
First No. = 6 × 3 = 18
2nd No.   = 3 × 3 =  9
3rd No.   = 3