Average questions

Averages are a common topic in Aptitude questions. Solving problems on averages might be difficult and requires a good grasp of the concept. The key to solving these questions lies in understanding the basics of averaging and how to apply the concept to the given problem. A few Aptitude Questions and Answers on Problems on Averages are given below.

  1. The average of 4 findings is 31 and the average of 6 findings is 29. Find the average of all the 10 findings:

Answer: Option C

Total average = \(\frac{4 \times 31 + 6 \times 29}{10}\)

= 29.8

  1. The average weight of five persons sitting in a boat is 38 kg. The average weight of the boat and the persons sitting in the boat is 52kg. What is the weight of the boat ?

Answer: Option B
  • Average weight of 5 persons = 38 Kg
  • ∴ Total weight of these five persons = 38 × 5 = 190 Kg

  • Now, average weight of (the boat + 5 persons)

    = 52 kg

  • ∴ Total weight of (the boat + 5 persons) = 52 × 6 = 312 Kg.
  • ∴ Weight of the boat = 312 - 190 = 122 Kg.
  1. What is the average of the squares of the first 19 natural numbers?

Answer: Option B

\( 1^{2}+2^{2}+3^{2}+\cdots+n^{2}\)

\(=\frac{n(n+1)(2 n+1)}{6}\)

Their average \(=\frac{(n+1)(2 n+1)}{6}\)

\(=\frac{(19+1)(2 \times 19+1)}{6}\)

(Here \(n=19)\)

\(=\frac{20 \times 39}{6}=130\)

  1. What is average of first 11 prime numbers?

Answer: Option C

First 11 prime numbers are \(\Rightarrow 2,3,5,7,11,13,17,19,23,29\) and 31

Their sum \(=2+3+5+7+11+\)

\(13+17+19+23+29+31=160\)

\(\therefore\) Required average \(=\frac{160}{11}\)

\(=14.54\)

  1. The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is:

Answer: Option B

Let three consecutive even numbers be \(x, x+2\) and \(x+4\) According to the question,

\((x+x+2+x+4)-\frac{x+x+2+x+4}{3}\) \(=28\)

\(\Rightarrow(3 x+6)-\frac{3 x+6}{3}=28\)

\(\Rightarrow(3 x+6)-(x+2)=28\)

\(\Rightarrow 3 x+6-x-2=28\)

\(\Rightarrow 2 x+4=28\)

\(\Rightarrow 2 x=28-4=24\)

\(\Rightarrow x=\frac{24}{2}=12\)