Simple Average MCQ Quiz - Objective Question with Answer for Simple Average - Download Free PDF

Given:

The arithmetic mean of the weights of 14 students in a class is 42 kgs.

Mean weight increases by 600 grams (0.6 kgs) when the teacher's weight is included.

Formula used:

Mean = Total Weight / Number of People

Calculation:

Let the weight of the teacher be T.

Total weight of 14 students = 42 × 14 = 588 kgs

When the teacher is included, the mean weight becomes 42.6 kgs for 15 individuals.

Total weight (including teacher) = 42.6 × 15 = 639 kg

⇒ Teacher's weight (T) = Total weight (including teacher) - Total weight of 14 students

⇒ T = 639 - 588 = 51 kgs

∴ The correct answer is option (4).

Given:

Average weight of 271 fertilizer bags = 71 kg

Including the weight of the box, the average increases by 0.8 kg

Number of bags = 271

Formula used:

Total weight = Average × Number of items

Weight of the box = (New total weight) - (Old total weight)

Calculation:

Old total weight = 71 × 271 = 19241 kg

New average = 71 + 0.8 = 71.8 kg

New total weight = 71.8 × 271

⇒ New total weight = 19457.8 kg

Weight of the box = New total weight - Old total weight

⇒ Weight of the box = 19457.8 - 19241 = 216.8 kg

∴ The correct answer is option (1).

Given:

The average weight of a kabaddi team of 121 players = 71 kg

The average weight increases by 1 kg when the manager is included

Formula used:

New average = (Total weight of players + Weight of manager) / (Number of players + 1)

Calculation:

Total weight of the team (players only) = 121 × 71 = 8591 kg

New average weight = 71 + 1 = 72 kg

⇒ (Total weight of players + Weight of manager) / (121 + 1) = 72

⇒ (8591 + Weight of manager) / 122 = 72

⇒ 8591 + Weight of manager = 72 × 122

⇒ 8591 + Weight of manager = 8784

⇒ Weight of manager = 193 kg

∴ The correct answer is option (3).

Given:

Class 1: Number of students = 75, Average marks = 75

Class 2: Number of students = 80, Average marks = 80

Class 3: Number of students = 85, Average marks = 85

Formula used:

Overall average = \(\frac{\text{Sum of marks of all classes}}{\text{Total number of students}}\)

Calculation:

Sum of marks for Class 1 = 75 × 75 = 5625

Sum of marks for Class 2 = 80 × 80 = 6400

Sum of marks for Class 3 = 85 × 85 = 7225

Total sum of marks = 5625 + 6400 + 7225 = 19250

Total number of students = 75 + 80 + 85 = 240

⇒ Overall average = \(\frac{19250}{240}\)

⇒ Overall average = 80.2083 (approximately)

∴ The correct answer is option (1).

Given:

Average weight of P, Q, and R = 54 kg

Average weight of P and Q = 48 kg

Average weight of Q and R = 49 kg

Formula used:

Sum of averages = Average × Number of terms

Calculations:

Total weight of P, Q, and R = 54 × 3 = 162

Total weight of P and Q = 48 × 2 = 96

Total weight of Q and R = 49 × 2 = 98

⇒ Weight of Q = weight of (Q + R) + weight of (P + Q) – weight of (P + Q + R)

⇒ Weight of Q = 98 + 96 - 162

⇒ Weight of Q = 32

The correct answer is Option (1).

Given :

Average = 18.5 kg

Decrease in Average = 15.5 kg

Formula Used :

Average = Sum of all observations/Number of observations

Calculation : 

Sum of 32 Students = 18.5 × 32 = 592

Sum When 4 Students Left = 15.5 × 28 = 434

Difference = 592 - 434 = 158

Average = 158/4 = 39.5

∴ The correct answer is 39.5.

Given:

The average marks of 60 students are 62

The average marks of the boys = 60

The average marks of the girls = 65

Formula used:

Average = Sum of observation/Total number of observation

Calculation:

Let the no. of boys in the class be X

The no. of girls in the class be (60 - X).

According to the questions,

65 × (60 - X) + (60 × X) = (60 × 62)

⇒ 3900 - 65X + 60X = 3720

⇒ 180 = 5X

⇒ X = 36

So, the number of boys = 36

∴ The number of boys in the class is 36.

Shortcut Trick

Here, (3 + 2) = 5 unit → 60 students

Then, 3 unit → 60/5 × 3 = 36 students (Boys)

Given:

The average weight of 49 students in a class is 39 kg.

Concept used:

Average = Sum of elements/Number of elements

Calculation:

Total weight of the 49 students = 39 × 49

⇒ 1911

According to the question,

New total weight = 1911 - 40 × 7 + 54 × 7

⇒ 1911 - 280 + 378

⇒ 2009

New average = 2009/49

⇒ 41 kg

∴ The new average weight (in kg) of the class is 41.

Shortcut Trick

Seven students of average weight 40 kg leave and Seven students of average weight 54 kg join.

So, net weight gain (54 - 40) × 7 = 98 kg

This extra will be distributed among 49 people, so average will increase 98/49 = 2 kg

The new average weight 39 + 2 = 41 kg

Calculation:

According to Raghav, his weight is more than 64 kg but less than 74 kg. 

i.e. 64 < Weight <74

His sister  thinks that his weight is more than 60 kg but less than 69 kg.

i.e. 60 < Weight < 69

His mother's view is that his weight cannot be more than 68 kg

i.e. Weight <= 68.

His father's view is that his weight cannot be more than 67 kg.

i.e. Weight <= 67.

So possible weights are 65, 66, 67

Only possible average is (65 + 66 +67) / 3 = 66kg

∴ The correct option is 1

Given:

A company employed 700 men and 300 women and the average wage was Rs. 450 per day.

A man got Rs. 50 more than a woman.

Calculation:

Let the wages of each man and woman be (x + 50) and x respectively.

Using mixture and allegation, 

​According to the question,

(450 - x) : (x - 400) = 700 : 300

Taking ( -) common 

(x - 450) : (400 - x) = 700 : 300

⇒ (x - 450) : (400 - x) = 7 : 3

⇒ 3x - 1350 = 2800 - 7x

⇒ 10x = 4150

⇒ x = 415

∴ The daily wage of the women is Rs. 415.

Given:

The average weight of apples in the original basket = 50 kg

Additional apples added = 6

The average weight of the additional apples = 60 kg

Increase in average weight = 5 kg

Formula:

To calculate the average, we divide the sum of all the values by the total number of values.

Solution:

Let's assume the number of apples in the original basket is 'n'.

(50n + 6 × 60)/(n + 6) = 50 + 5

(50n + 360)/(n + 6) = 55

50n + 360 = 55n + 330

5n = 30

n = 6

Therefore, the number of apples in the basket originally is 6.

Calculation

Let the number of students in senior school be a.

The total amount charged from students of junior school = 325 × 80

⇒ 26000

The total amount charged from students of senior  school = 400 × a

⇒ 400a

The total amount charged from both the schools = (a + 80) × 352

⇒ (a + 80) × 352 = 2600 + 400a

⇒ 400a - 352a = 28160 - 26000

⇒ 48a = 2160 

⇒ a = 45.

The number of students from the senior school who went on the excursion is 45.

Shortcut Trick

Given:

There are 15 students in a class.

Their average weight is 40 kg.

When one student leaves the class, the average weight is 39.5 kg.

Calculation:

The total weight of 15 students is 15 × 40 = 600 kg

The total weight of 14 students is 14 × 39.5 = 553 kg

The weight of new students is 600 - 553 = 47 kg

∴ The correct option is 1

Given : 

B buys 10 pens for ₹8 each.

10 erasers for ₹5 each.

Some sharpeners for ₹4 each.

Formula Used : 

Average = Sum of all observations/Number of observations

Calculation : 

⇒ 150 = 10 × 8 + 10 × 5 + 4 × x

⇒ 150 = 80 + 50 + 4x

⇒ 4x = 20

⇒ x = 5

Average = 150/(5 + 10 + 10) = 150/25 = 30/5 = 6

∴ The correct answer is 6.

Given:

Ram, Shyam, Rohan, Reeta, and Mukesh are five members of a family who are weighed consecutively and their average weight is calculated after each member is weighed.

The average weight increases by 2 kg each time.

Concept used:

Total = Average × Number of entities

Calculation:

Let the weight of Ram be Q kg.

Average weight = Q kg

According to the question,

After adding Shyam, the average weight = (Q + 2) kg

Weight of Shyam = 2(Q + 2) - Q = (Q + 4) kg

After adding Rohan, the average weight = (Q + 4) kg

Weight of Rohan = 3(Q + 4) - Q - (Q + 4) = (Q + 8) kg

After adding Reeta, the average weight = (Q + 6) kg

Weight of Reeta = 4(Q + 6) - Q - (Q + 4) - (Q + 8) = (Q + 12) kg

After adding Mukesh, the average weight = (Q + 8) kg

Weight of Mukesh = 5(Q + 8) - Q - (Q + 4) - (Q + 8) - (Q + 12) = (Q + 16) kg

Now, Mukesh is heavier than Ram by = (Q + 16) - Q = 16 kg

∴ Mukesh is heavier than Ram by 16 kg.