# 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,

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

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

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

$\Rightarrow 3 x+6-x-2=28$

$\Rightarrow 2 x+4=28$

$\Rightarrow 2 x=28-4=24$

$\Rightarrow x=\frac{24}{2}=12$