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

Given:

Average of nine numbers = m

Average of three numbers of the nine numbers = p

Average of the remaining numbers = n

To find:

Find the correct option out of the given option.

Solution:

Since average of nine numbers = m

Sum of 9 numbers = m*9

Average of three of the 9 numbers = p

Their sum = 3p

Average of the remaining numbers = n

Their sum = 6n

Sum of total 9 numbers = sum of 3 nos. + sum of 6 nos.

9m = 3p + 6n

3m = p + 2n

Therefore the correct option is option 3.

Answer 2

Given :- 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

Solution :-

we know that,

• Average = (sum of observation) / (Total number of observation.)

So,

→ Average of 9 numbers = m .

then,

→ sum of 9 numbers = 9 * m = 9m .

similarly,

→ Average of 3 numbers = p .

then,

→ sum of 3 numbers = 3 * m = 3p .

and,

→ Average of remaining 6 numbers = n .

then,

→ sum of 6 numbers = 6 * n = 6n .

therefore,

→ Sum of 9 numbers = sum of 3 numbers + sum of 6 numbers

→ 9m = 3p + 6n

→ 9m = 3(p + 2n)

dividing both sides by 3,

→ 3m = p + 2n

→ 3m = 2n + p (C) (Ans.)

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