## Problems on Averages Set - 2

1. In the first 10 over’s of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 over’s to reach the target of 282 runs?
a) 6.25
b) 6.50
c) 6.75
d) 7
e) None of these
2. 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 ears. What is the average age of the family?
a) 28 7/4 years
b) 31 7/5 years
c) 32 1/7 years
d) can’t be determined
e) None of these
3. 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
e) None of these
4. 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
e) None of these
5. 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) 76Kg
b) 76.5Kg
c) 85Kg
e) None of these
6. 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) 25years
e) None of these
7. 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 Rs5200. The monthly income of P is:
a) 3500
b) 4000
c) 4050
d) 5000
e) None of these
8. 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
e) None of these
9. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per liter for three successive years. What approximately is the average cost per liter of petrol if he spends Rs. 4000 each year?
a) Rs. 7.98
b) Rs. 8
c) Rs. 8.50
d) Rs. 9
e) None of these
10. In Arum’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arum and he thinks that Arum’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 Arum?
a) 67 kg
b) 68 kg
c) 69 Kg.
e) None of these
Solutions:
1. A) Required average = [282 – (302 × 10)]/40 = 250/40 = 6.25
2. E) Required average = [(67 × 2 + 35 × 2 + 6 × 3)/(2 + 2 + 3)] = [(134 + 70 + 18)/7] = 222/7 = 31 5/7
3. A) 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
4. D) Average of 20 numbers = 0
Therefore, Sum of 20 numbers (0 × 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)
5. C) Total weight increased = (8 × 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
6. A) 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
7. B) 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
8. B) 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
9. A) Total quantity of petrol = [(4000/7.5) + (4000/8) + (4000/8.5)]
Consumer in 3 years = 4000 [(2/15 + 1/8 + 2/17)] litres = 76700/51
Total amount spent = Rs. (3 x 4000) = Rs. 12000
Average Cost = Rs.[(12000 x 51)/76700] = Rs. 6120/767 = 7.98
10. A) 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
Therefore, required average = (66 + 67 + 68)/3 = 201/3 = 67kg

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