AVERAGES TEST

1.A cricketer has a mean score of 58 runs in nine innings. Find out how many runs are to be scored by him in the tenth innings to raise the mean score to 61.

A. 28                                             B. 48

C. 88                                             D. 89

ANSWER & EXPLANATION

ANSWER:C
Explanation
Mean score of 9 innings = 58 runs.
Total score of 9 innings = (58 x 9) runs = 522 runs.
Required mean score of 10 innings = 61 runs.
Required total score of 10 innings = (61 x 10) runs = 610 runs.
Number of runs to be scored in the 10th innings
= (total score of 10 innings) - (total score of 9 innings)
= (610 -522) = 88.
Hence, the number of runs to be scored in the 10th innings = 88.

2. 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

ANSWER & EXPLANATION

ANSWER:C
Solution:
Total weight increased = (8 x 2.5) kg = 20 kg
Weight of new person = (65 + 20) kg = 85 kg

3. 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 & EXPLANATION

ANSWER: D
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).

4. 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. 26kg                                                   D.31 kg

ANSWER & EXPLANATION

ANSWER: C
A. 17 kg B. 20 kg C. 26 kg D. 31 kg Answer & Explanation 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.

5. There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re What was the original expenditure of the mess?

A. 430                                              B.620

C.420                                               D. 520

ANSWER & EXPLANATION

ANSWER: C
Let the original average expenditure be Rs.xx then, 42(x−1)−35x=4242(x−1)−35x=42
⇒7x=84⇒7x=84
⇒x=12⇒x=12
Therefore original expenditure
=Rs.(35×12)=Rs.(35×12) = Rs 420

6.Average of 10 matches is 32, How many runs one should should score to increase his average by 4 runs.

A. 70                                                    B.78

C. 76                                                    D. 80

ANSWER & EXPLANATION

ANSWER: C
Average after 11 innings should be 36
So, Required score = (11 * 36) - (10 * 32)
= 396 - 320 = 76

7 .The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is z, then

A. x = y + z                                         
B. 2x = y + z
C. x = 2y + z                                           
D.x = y + 2z

ANSWER & EXPLANATION

ANSWER :B
Explanation:
X =((3y+3z)/6) or 2X= y + z

8.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                                                   B.24

C. 26                                                    D. 27

ANSWER & EXPLANATION

ANSWER: 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.

9.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 is the weight of the new person?

A. 75                                                    B.85

C. 50                                                    D. 80

ANSWER & EXPLANATION

ANSWER: B
Total increase in weight = 8 × 2.5 = 20
If xx is the weight of the new person, total increase in weight = x−65x−65
=> 20 = xx - 65
=> xx = 20 + 65 = 85

10. A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?

A.39                                                    B.35

C. 38                                                    D. 40

ANSWER & EXPLANATION

ANSWER: A
DETAILED SOLUTION
Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 87 = Total runs scored in 17 innings => 16(x-3) + 87 = 17x
=> 16x - 48 + 87 = 17x
=> x = 39

11.The mean of 25 observations is 36. If the mean of the first observations is 32 and that of the last 13 observations is 39, find the 13th observation.

A. 24                                     B. 25 and 4

C. 28                                                    D. 23

ANSWER & EXPLANATION

ANSWER: D
Mean of the first 13 observations = 32.
Sum of the first 13 observations = (32 × 13) = 416.
Mean of the last 13 observations = 39.
Sum of the last 13 observations = (39 × 13) = 507.
Mean of 25 observations = 36.
Sum of all the 25 observations = (36 × 25) = 900.
Therefore, the 13th observation = (416 + 507 - 900) = 23.
Hence, the 13th observation is 23.