SSC CGL (Prelims) Maths: Averages questions with solutions

Q1. The average weight of 8 men increases by 2 kg when one of the men who weighs 60 kg is replaced by a new man. What is the weight of the new man?

1. 74 kg
2. 76 kg
3. 78 kg
4. 72 kg

Answer: 76 kg

If the average weight of 8 men increases by 2 kg, the total weight increases by 8 × 2 = 16 kg. Since one 60 kg man is replaced, the new man's weight must be 60 + 16 = 76 kg.

Q2. The average of the first five multiples of 6 is:

1. 12
2. 18
3. 24
4. 20

Answer: 18

The first five multiples of 6 are 6, 12, 18, 24, and 30. Their sum is 90, and dividing by 5 gives 18. So the average is 18.

Q3. 4 boys and 3 girls spent ₹120 on average, of which the boys spent ₹150 on average. Then the average amount spent by the girls is:

1. ₹ 80
2. ₹ 60
3. ₹ 90
4. ₹ 100

Answer: ₹ 80

The total spent by 7 children is 7 × 120 = 840. The boys spent 4 × 150 = 600, so the girls spent 840 - 600 = 240; dividing by 3 gives 80.

Q4. The mean of 9 observations is 16. One more observation is included and the new mean becomes 17. The 10th observation is:

1. 9
2. 16
3. 26
4. 30

Answer: 26

The sum of 9 observations is 9 × 16 = 144. The sum of 10 observations is 10 × 17 = 170, so the 10th observation is 170 - 144 = 26.

Q5. The average of eight successive numbers is 6.5. The average of the smallest and the greatest numbers among them will be:

1. 4
2. 6.5
3. 7.5
4. 9

Answer: 6.5

For eight successive numbers, the average is the midpoint of the sequence. Therefore, the average of the smallest and greatest numbers is the same as the average of all eight numbers. Hence it is 6.5.

Q6. The average of five consecutive positive integers is \(n\). If the next two integers are also included, then the average of all these integers will:

1. Increased by 1.5
2. Increased by 1
3. Remain the same
4. Increase by 2

Answer: Increased by 1

If the five consecutive integers are \(x-2, x-1, x, x+1, x+2\), their average is \(x=n\). Adding the next two integers gives \(x+3\) and \(x+4\), so the new average becomes \(x+1\). Thus the average increases by 1.

Q7. The average of the first nine integral multiples of 3 is:

1. 12
2. 15
3. 18
4. 21

Answer: 15

The first nine multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27. Their average is the midpoint of 3 and 27, which is 15.

Q8. The average of odd numbers up to 100 is:

1. 49
2. 49.5
3. 50
4. 50.5

Answer: 50

The odd numbers up to 100 are 1, 3, 5, ..., 99. This is an arithmetic progression, so its average is the midpoint of the first and last terms: \((1+99)/2=50\).

Q9. The average of nine consecutive odd numbers is 53. The least odd number is:

1. 22
2. 27
3. 35
4. 45

Answer: 45

For nine consecutive odd numbers, the average is the 5th term. So the middle number is 53. The least odd number is 4 steps below it: \(53-8=45\).

Q10. The average salary of all the workers in a workshop is ₹8000. The average salary of 7 technicians is ₹12,000 and the average salary of the rest is ₹6000. The total number of workers in the workshop is:

1. 20
2. 21
3. 22
4. 23

Answer: 21

Let the total number of workers be \(n\). Then total salary is \(8000n\). The 7 technicians earn \(7\times 12000=84000\), and the remaining \(n-7\) workers earn \(6000(n-7)\). Equating totals gives \(8000n=84000+6000(n-7)\), so \(n=21\).

Q11. Of the three numbers, the first is 4 times the second and 3 times the third. If the average of all three numbers is 95, what is the third number?

1. 57
2. 76
3. 130
4. 60

Answer: 60

Let the third number be \(x\). Then the first number is \(3x\) and the second is \(\frac{3x}{4}\). Their average is 95, so \(\frac{3x+\frac{3x}{4}+x}{3}=95\), which gives \(x=60\).

Q12. Of the three numbers, the first is twice the second and the second is twice the third. The average of the three numbers is 21. The smallest of the three numbers is:

1. 6
2. 9
3. 12
4. 18

Answer: 9

Let the third number be \(x\). Then the second is \(2x\) and the first is \(4x\). Their average is \(\frac{4x+2x+x}{3}=21\), so \(7x=63\) and \(x=9\). The smallest number is 9.