Averages(Quantitative Aptitude ) Questions and answers for exam Preparation

Quantitative Aptitude

AVERAGES MCQs

Averages

Total Questions : 3752 | Page 7 of 376 pages

A batsman in his 17th innings makes a score of 85, and thereby increases his average by 3. What is his average after 17 innings?

Discuss Question

Answer: Option B. -> 37
- Let the average after 16th innings be a, then total score after 17th innings =>

16a+85 = 17 (a+3)

a = 85-51 = 34

Average after 17 innings = a + 3 = 34 + 3 = 37

Question 62.

A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?

Discuss Question

Answer: Option D. -> 49
- Total of 10 innings = 21.5 x 10 = 215
Suppose he needs a score of a in 11th innings; then average in 11 innings =
215 + a = 24 11

or, a = 264-215 = 49

Question 63.

1/3 rd of certain journey is covered at the rate of 25 km/hr, 1/4 th at the rate of 30 km/hr and rest at 50 km/hr. Find the averae speed for the whole journey?

Discuss Question

Answer: Option B. -> 33 1/3 km/hr
- Let the journey by a km. Then a/3 km at the speed of 25 km/hr and a/4 km at 30 km/hr and the rest distance ( a- a/3 –a/4 ) = 5/12 x a at the speed of 50 km/hr.

Total time taken during the journey of a km
a + a + 5a = 18a = 3a 3 x 25 4 x 30 12 x 50 600 100

Question 64.

The average salary of the entire staff in a office is Rs 120 per month. The average salary of officers is Rs 460 and that of non officer is Rs 110. If the number of officer is 15, then find the number of non-officer in the office?

Discuss Question

Answer: Option C. -> 510

- Let the required number of non-officers = a

Then, 110a + 460 x 15 = 120 (15 + a)

or, 120a – 110a = 450 x 15 – 120 x 15 = 15 (460 – 120)

or, 10a = 15 x 340; a = 15 x 34 = 510

Average salary of the entire staff in a office = Rs 120
Average salary of officers = Rs 460
Average salary of non-officer = Rs 110
Number of officers = 15

We can find the number of non-officers by using the formula for weighted average.
Weighted Average = ( Weight1 × Average1 + Weight2 × Average2 ) / (Weight1 + Weight2)

Weight1 = Number of officers = 15
Average1 = Average salary of officers = Rs 460

Weight2 = Number of non-officers = ?
Average2 = Average salary of non-officer = Rs 110

Substituting the given values in the above formula, we get
Weighted Average = ( 15 × 460 + Weight2 × 110 ) / (15 + Weight2) = 120

15 × 460 + Weight2 × 110 = 120 (15 + Weight2)

1740 + 110 Weight2 = 120 (15 + Weight2)

1740 + 110 Weight2 = 1800 + 120 Weight2

-120 Weight2 = 1800 - 1740

-120 Weight2 = 60

Weight2 = 60 / -120

Weight2 = -0.5

Number of non-officers = Weight2 = -0.5

Since, we cannot have -0.5 non-officers, we can take the nearest integer value.

Number of non-officers = Weight2 = -0.5 ≈ 0

Number of non-officers = 0

Thus, the number of non-officers in the office = 0

Hence, the correct answer is Option C. 510

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 65.

There were 35 students in a hostel. If the number of students increase by 7, the expenses of the mess increase by Rs 42 per day while the average expenditure per head diminishes by Rs 1. Find the original expenditure of the mess?

Discuss Question

Answer: Option B. -> 420
- Suppose the average expenditure was Rs a.
Then total expenditure = 35a

When 7 more students join the mess, total expenditure = 35a + 42

Now, the average expenditure= (35a+42) / (35 + 7)

Now, we have (35a + 42)/ 42 =(a - 1)

or, 35a + 42 = 42a – 42

7a = 84

a = 12

Thus the original expenditure of the mess = 35 x 12 = 420

Question 66.

Find the average of first 40 natural numbers?

Discuss Question

Answer: Option C. -> 820
- Average = n (n+1) = 40 x 41 = 820 2 2

Question 67.

Find the average of first 20 multiple of 7?

Discuss Question

Answer: Option B. -> 73.5
- Average = 7 (1+2+3+…….+20) = 7 x 20 x 21 = 73.5 20 20 x 2

Question 68.

The average of four consecutive even number is 27. Find the largest of these numbers?

Discuss Question

Answer: Option C. -> 30
-  Let the numbers be x, x+2, x+4, x+6

Average = x+(x+2)+(x+4)+(x+6) = 27 4 = 4x+12 = 27 4                                                 x = 24

Largest number = (x+6) = 24+6 = 30

Question 69.

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:

Discuss Question

Answer: Option B. -> 54.68
- Aaverage = 55 x 50 + 60 x 55 + 45 x 60 55 + 60 + 45 = 2750 + 3300 + 2700 160 = 8750 160 = 54.68

Question 70.

The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, find the weight of B?

Discuss Question

Answer: Option B. -> 31
-

Let A, B, C represent their respective weights. Then, we have:

A + B + C = (45 x 3) = 135 .... (i)

A + B = (40 x 2) = 80 .... (ii)

B + C = (43 x 2) = 86 ....(iii)