Average - Aptitude MCQ Questions and Solutions with Explanations

Answer: Option C

According to the question,
As we know that average of 'n' positive integer is
= $$\frac{n(n + 1)}{2 × n}$$
= $$\frac{(n + 1)}{2}$$
Here n = 100
∴ $$\frac{100 + 1}{2}$$
= $$\frac{101}{2}$$
= 50.5

Answer: Option B

Sum of age of two players = 17 + 20 = 37 years
Decreasing age of players = 11 × 2 = 22 months
Sum of age of two new players
= 37 years - 22 months
= 35 years 2 months
Average = 17 years 7 months

Alternate :
$$\frac{{\left( {17 + 20} \right) - \left( {{\text{Sum of two new players}}} \right)}}{{11}}$$
= $$\frac{2}{12}$$
= $$\frac{1}{6}$$
Sum of two new players = $$\frac{211}{6}$$
Average of two new players
= $$\frac{211}{12}$$
= 17 years 7 months

Answer: Option C

According to the question,
The mean of 50 numbers is = 30
Sum of 50 numbers is = 50 × 30 = 1500
Later it was discovered that two entries were wrongly entered as 82 and 13 instead of 28 and 31.
∴ Difference = (82 + 13) - (28 + 31)
= 95 - 59
= 36 (extra)
∴ Actual sum of 50 numbers is = 1500 - 36 = 1464
∴ Actual average = $$\frac{1464}{50}$$   = 29.28

Answer: Option A

Series:- a, a + 2, a + 4.....
Sum = na + 2 + 4 + ..... upto n terms
Sum = na + S_n
$${S_n} = \frac{{2\left( {{2^n} - 1} \right)}}{{2 - 1}}$$
Average = $$a + \frac{{2\left( {{2^n} - 1} \right)}}{n}$$

Answer: Option B

Let the age of younger boy = x years
Then the age of older boy = (x + 5)
According to the question,
⇒ (30 × 15) - 20 + x + x + 5 = 31 × 15
⇒ 430 + 2x + 5 = 465
⇒ 2x = 30
⇒ x = 15