The average of a set of numbers reduces from 14 to 11 when the number 35 is removed.

The average of a set of numbers reduces from 14 to 11 when the number 35 is removed. How many numbers were in the original set?
(a) 8
(b) 11
(c) 21
(d) 25

Anurag Mishra Professor Asked on 29th February 2016 in Maths.
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1 Answer(s)

Answer: (a) 8 

Solution:-
Let the original number of a set = X and sum of number of a set be S
Then, the average of numbers = S/X

14 = S/X
S = 14 X          …………(1)

New average is 11 when the number 35 is removed from set.
Then, 11 = S – 35/(X – 1)
S – 35 = 11 X – 11
S – 11 X = 35 – 11
S – 11 X = 24

From Equation (1), S = 14 X
Then, 14 X – 11 X = 24
3 X = 24
X = 24/3
X = 8

Then, the original number of a set is 8.

Hence, the correct answer is option (a) 8.

Anurag Mishra Professor Answered on 4th March 2016.
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