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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