Average - Aptitude MCQ Questions and Solutions with Explanations

Let the number of wickets = x
According to question,
⇒ 24.85x + 52 = 24 (x + 5)
⇒ 24.85 x + 52 = 24x + 120
⇒ 0.85x = 68
⇒ x = $$\frac{69 × 100}{85}$$
⇒ x = 80
Number of wickets till the last match is
= x + 5
= 80 + 5
= 85

According to the question,
Average of 'n' number's x₁, x₂.....x_n is $$\overline x $$
Sum of n numbers = n$${\overline x }$$
∴ $$\sum\limits_{i\, = \,1}^n {} \left( {{x_1} - \overline x } \right)$$
Put i = 1, 2, 3.....n then
{x₁ + x₂ + x₃ + .....(xn - n$${\overline x }$$)}
As we know that
x₁ + x₂ + x₃+.....+ x_nx = n$${\overline x }$$
= (n$${\overline x }$$ - n$${\overline x }$$)
= 0

According to the question
Average number of visitors on sunday = 510
Average number of visitors on other days = 240
∴ If month start on sunday then there are five sundays in a month and 25 other days.
∴ Number of visitors on sundays = 510 × 5 = 2550
Number of visitors on other days = 240 × 25 = 6000
∴ Average visitors = $$\frac{2550 + 6000}{30}$$   = 285

According to the question,
Average weight of whole class
= $$\frac{42 × 25 + 28 × 40}{70}$$
= $$\frac{1050 + 1120}{70}$$
= 31 kg

According to the question,
Average of x number is y²
∴ Sum of x number is = xy²
Average of y number is = x²
∴ Sum of y number is = yx²
Average of all number is
= $$\frac{{{xy^2} + {yx^2}}}{{x + y}}$$
= $$\frac{{xy\left( {x + y} \right)}}{{x + y}}$$
= xy

According to the question,
Average = $$\frac{1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 7 + 7 + 7}{28}$$
Average = $$\frac{1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6 + 7 × 7}{28}$$
Average = $$\frac{1 + 4 + 9 + 16 + 25 + 36 + 49}{28}$$
Average = 5

Let the weight of 1 student = x kg
The weight to 15 student = 15x kg
Let the weight of new comer = y kg
∴ According to the question,
⇒ 15x - 40 + y = 15 (x + 1.5)
⇒ 15x - 40 + y = 15x + 22.5
⇒ y = 62.5 kg

Let the score in the eleventh innings = x
According to the question,
⇒ $$\frac{60 × 10 + x}{11}$$  = 62
⇒ 600 + x = 682
⇒ x = 82

Let eight consecutive numbers are
= 1, 2, 3, 4, 5, 6, 7, 8 sum
= 36 units two middle numbers are
= 4 + 5
= 9 units
Average of two middle numbers = 6 (Given)
Sum of two middle numbers = 6 × 2 = 12
∴ 9 units → 12
1 unit → $$\frac{12}{9}$$
∴ 36 units → $$\frac{12}{9}$$ × 36 = 48
∴ Sum of all consecutive number = 48

Tue + Wed + Thu = 41° × 3 = 123°.....(i)
Wed + Thu + Fri = 40° × 3 = 120° .....(ii)
(i) - (ii)
After solving both, we get
Tue - Fri = 3°
Tue = 3° + Fri
= 3° + 39°
= 42°