Average

 Average ( SET 4 : Q16-Q20 )

16. The average of a certain set of x numbers is y and the average of a certain set of y numbers is x. The average of all the numbers taken together is
1

Incorrect
2

Correct Answer
3

4

Solution: 2

Let the sum of the nos. in the first set be N, and that of the second set be M.

⇒ N/x = y, and M/y = x

⇒ N = xy, and M = xy.

⇒ M + N = 2xy

Since there are x + y numbers, we have

Average = (M+N)/(x+y) = 2xy/(x+y)

17. The average marks secured by 55 boys was 67. But it was discovered that an item 85 was misread as 30. What is the correct mean of marks?
1
65.5
2
63.5
Incorrect
3
68.0
Correct Answer
4
67.5

Solution: 3

Average marks secured by 55 boys = 67

Total marks secured by 55 boys = 67 × 55 = 3685

An item 85 is misread as 30

⇒ New average = (3685 - 30 + 85)/55 = 3740/55 = 68

∴ The Correct mean of marks = 68

Smart trick

New average = Old average + (Error/Number of boys) = 67 + (85 - 30)/55 = 67 + (55/55) = 67 + 1 = 68

18. A batsman in his 12th innings makes a score of 79 runs and thereby increase his average score by 1. What is his average after the 12th innings?
1
71
2
65
Incorrect
3
67
4
68
Correct Answer

Solution: 4

Let average score of first 11 innings be x runs.

Then, total runs made by the batsman in 11 innings = 11x

According to the question, after 12th inning, average score = x + 1


⇒ 79 + 11x = 12x + 12

⇒ x = 79 – 12 = 67

Thus, average score after 12th inning = 67 + 1 = 68 runs.

19. Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 63, then difference of first and third numbers is:
1
27
2
50
Incorrect
3
54
Correct Answer
4
48

Solution: 3

Let the second number be x

∵ first number is twice the second, the first number = 2x

Also, since first number is half of the third, third number = 4x

Now, the average of the 3 numbers is 63.

We know that, average = Sum of all quantities/Number of quantities

∴ (2x + x +4x)/3 = 63

⇒ 7x =189

⇒ x = 27

Thus, the numbers are 54, 27 and 108

The difference of first and third number = 108 – 54 = 54

20. Rahul Dravid has a certain average for 13 innings. When he plays the 14th inning he scores 150 runs and his average increases by 3 runs. What is the new average?
1
108
2
120
3
113
Incorrect
4
111
Correct Answer

Solution: 4

Let the old average be x runs

We know that,

Average = Sum of observations/No. of observations

∴ Sum of runs scored in 13 innings = Average × No. of innings

⇒ Sum of runs = x × 13 = 13x

Runs scored in the 14th inning = 150

New average = x + 3

∴ Sum of runs = (x + 3) × 14 = (14x + 42)

Now, 13x + 150 = 14x + 42

∴ x = 150 – 42 = 108

⇒ New average = x + 3 = 108 + 3 = 111 runs

 SET 01 : Q1 - Q5

 SET 02 : Q6 - Q10

 SET 03 : Q11 - Q15

 SET 04 : Q16 - Q20

 SET 05 : Q21 - Q25


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