Average Related Problems
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.|
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.
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