Average Related Problems (Quantitative Reasoning)

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:

① Sum of Quantities = Number of quantities × Average

② Average is also called the Arithmetic Mean.

③ If all the given quantities have the same value, then the vaue itself is the average.

④ If each of the given quantities is increased/decreases by a constant N, then their average is also increased/decreased by N.

⑤ 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