# AVERAGE

## Important formulas of average

**Average:**

Average = (Sum of observations/ Number of observations)

**Average Speed:**

Suppose a man covers a certain distance at x kmph and an equal distance at y kmph.

Then, the average speed during the whole journey is (2xy/x + y) kmph.

### MCQS

**In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?**

A. 6.25

B. 6.5

C. 6.75

D. 7

**Answer: Option A**

Explanation:

Required run rate =(282 – (3.2 x 10)) =250/40= 6.25

**A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?**

A. 28 4/7 years

B. 31 5/7 years

C. 32 1/7 years

D. None of these

**Answer: Option B**

Explanation:

Required average = (67 x 2 + 35 x 2 + 6 x 3/2 + 2 + 3) = (134 + 70 + 18/7)

222/7

= 31 5/7 years.

**A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?**

A. Rs. 4991

B. Rs. 5991

C. Rs. 6001

D. Rs. 6991

**Answer: Option A**

Explanation:

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

Required sale = Rs. [ (6500 x 6) – 34009 ]

= Rs. (39000 – 34009)

= Rs. 4991.

**The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?**

A. 0

B. 1

C. 10

D. 19

**Answer: Option D**

Explanation:

Average of 20 numbers = 0.

Sum of 20 numbers (0 x 20) = 0.

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th

number is (-a).

**The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?**

A. 76 kg

B. 76.5 kg

C. 85 kg

D. Data inadequate

E. None of these

**Answer: Option C**

Explanation:

Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

**The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?**

A. 23 years

B. 24 years

C. 25 years

D. None of these

**Answer: Option A**

Explanation:

Let the average age of the whole team by x years.

11x – (26 + 29) = 9(x -1)

11x – 9x = 46

2x = 46

x = 23.

So, average age of the team is 23 years.

**The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:**

A. 3500

B. 4000

C. 4050

D. 5000

Answer: Option B

Explanation:

Let P, Q and R represent their respective monthly incomes. Then, we have:

P + Q = (5050 x 2) = 10100 …. (i)

Q + R = (6250 x 2) = 12500 …. (ii)

P + R = (5200 x 2) = 10400 …. (iii)

Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .(iv)

Subtracting (ii) from (iv), we get P = 4000.

P’s monthly income = Rs. 4000.

**The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:**

A. 35 years

B. 40 years

C. 50 years

D. None of these

**Answer: Option B**

Explanation:

Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.

Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.

Husband’s present age = (90 – 50) years = 40 years.

**A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?**

A. Rs. 7.98

B. Rs. 8

C. Rs. 8.50

D. Rs. 9

**Answer: Option A**

Explanation:

Total quantity of petrol consumed in 3 years = (4000/7.50 + 4000/8 + 4000/8.50) litres

= 4000 (2/15 + 1/8+ 2/17) litres = (76700/51) litres

Total amount spent = Rs. (3 x 4000) = Rs. 12000.

Average cost = Rs. (12000 x 51/76700) = Rs. 6120/767 = Rs. 7.98

**In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?**

A. 67 kg.

B. 68 kg.

C. 69 kg.

D. Data inadequate

E. None of these

**Answer: Option A**

Explanation:

Let Arun’s weight by X kg.

According to Arun, 65 < X < 72

According to Arun’s brother, 60 < X < 70.

According to Arun’s mother, X <= 68

The values satisfying all the above conditions are 66, 67 and 68.

Required average =(66 + 67 + 68/3) =(201/3) = 67 kg.

**The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:**

A. 17 kg

B. 20 kg

C. 26 kg

D. 31 kg

**Answer: Option D**

Explanation:

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)

Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)

Subtracting (i) from (iv), we get : B = 31.

B’s weight = 31 kg.

**The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.**

A. 47.55 kg

B. 48 kg

C. 48.55 kg

D. 49.25 kg

**Answer: Option C**

Explanation:

Required average = (50.25 x 16 + 45.15 x 8/16 + 8) = (804 + 361.20/24) = 1165.20/24 = 48.55

**A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:**

A. 250

B. 276

C. 280

D. 285

**Answer: Option D**

Explanation:

Since the month begins with a Sunday, to there will be five Sundays in the month.

Required average = (510 x 5 + 240 x 25/30)

= 8550/30

= 285

**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:**

A. 53.33

B. 54.68

C. 55

D. None of these

**Answer: Option B**

Explanation:

Required average = 55 x 50 + 60 x 55 + 45 x 60/55 + 60 + 45) = (2750 + 3300 + 2700/160)

= 8750/160 = 54.68

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