The average of 7 consecutive number is n, if the next 2 number also included then the new average will be increased by ?a)0b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Solution:

The given information can be represented as:

Let the first number be x

So, the next 6 consecutive numbers will be x+1, x+2, x+3, x+4, x+5, x+6

According to the given condition, the average of these 7 consecutive numbers is n.

So, we can write:

(x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6)/7 = n

Simplifying this equation, we get:

7x + 21 = 7n

x = (7n - 21)/7

x = n - 3

So, the 7 consecutive numbers are:

n - 3, n - 2, n - 1, n, n + 1, n + 2, n + 3

If we add the next 2 numbers (n + 4, n + 5), then the new average will be:

(n - 3 + n - 2 + n - 1 + n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5)/9

Simplifying this equation, we get:

(9n + 9)/9

= n + 1

So, the new average will be increased by 1.

Therefore, the correct answer is option B (1).

Answer

Avg of 7 no= (7+1)/2 = 8/2 = 4
Avg of 9 no = (9+1)/2 = 5
5- 4 = 1
Hence increased by 1

Similar Quant Doubts

A cricketer had an average number of runs as 32 after playing 10-innings. If he wants to make his average run rate increased by 4, then how much runs will he have to take in his next inning?

The average of seven consecutive even numbers is 10. If the next three even numbers are included, then what is the new average?

In the year 2016 the average number of people visited Goa per day is 73. In the next year number of visitors increased by 657. Then average number of people visited Goa in the year 2017 is ?

In a zumba class, the average age of all the members was 43.5 years. 10 members left the class and 6 new members joined. If the average age increased by 2 years and the total age decreased by 110, what was the number of members in the class initially?

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company