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
d) Data inadequate
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
d) Data inadequate
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
d) Data inadequate
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.
d) Data inadequate
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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