# 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

**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.