Question

The average of nine numbers is M and the average of three of these is P. If the average of remaining numbers is N, then

• A. M = N + P
• B. 2M = N + P
• C. 3M = 2N + P
• D. 3M = 2P + N

Answer 1

The Correct Option is C

To solve this problem, we need to find the relationship between M, N, and P based on the given conditions.

Let's denote the sum of nine numbers as S.

The average of these nine numbers is given by:

M = S/9

The sum of the nine numbers can be expressed as:

S = 9M

The sum of the three numbers, whose average is P, is:

3P

Let the sum of the remaining six numbers be S₁. The average of the remaining six numbers is N, hence:

N = S₁/6

Therefore, the sum of the remaining six numbers can be expressed as:

S₁ = 6N

Since the total of all nine numbers is:

S = 3P + 6N

We equate the two expressions for S:

9M = 3P + 6N

Dividing the entire equation by 3 gives:

3M = P + 2N

Hence, the correct relationship is:

3M = 2N + P