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__Averages Formulae__

1. Average

Average = (Sum of observations/Number of observations)

2. 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.

Average = (Sum of observations/Number of observations)

2. 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.

31. Find the average of the first 20 natural numbers?
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Answer: Option D

Explanation:

Average of the first 'n' natural numbers = (n + 1)/2

We get (20 + 1)/2 = 10.5

32. The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
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Answer: Option A

Explanation:

Sum of all the 13 numbers = 13 * 60 = 780

Sum of the first 7 of them = 7 * 57 = 399

Sum of the last 7 of them = 7 * 61 = 427

So, the 8th number = 427 + 399 - 780 = 46.

33. A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
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Answer: Option D

Explanation:

Let the average after the 16th inning be P.

So, the average after the 15th inning will be (P-3)
Hence, 15(P-30) + 64 = 16P => P = 19.

34. The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
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Answer: Option D

Explanation:

Sum of the marks for the class of 30 students = 30 * 40 = 1200

Sum of the marks for the class of 50 students = 50 * 60 = 3000

Sum of the marks for the class of 80 students =

1200 + 3000 = 4200

Average marks of all the students = 4200/80 = 52.5

35. The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
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Answer: Option C

Explanation:

Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)

Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)

(2)-(1) i.e. May - Jan = 2000

Salary of May is Rs.6500

Salary of January = Rs.4500