Question

The average of 16k numbers is 20. If 11k of the numbers are doubled and the remaining 5k numbers are tripled, find the percentage by which the average would increase.
a) 100%
b) 150%
C) 200%
d) 175%

Answer 1

Answer:

B .....................

Answer 2

Question :- The average of 16k numbers is 20. If 11k of the numbers are doubled and the remaining 5k numbers are tripled, find the percentage by which the average would increase.

a) 100%

b) 150%

C) 200%

d) 175%

e) None of these.

Solution :-

Let us assume that, each of the number is equal to 20.

than,

→ Average = (sum of numbers) / (Total numbers)

→ Average = (20 + 20 + _________ 16k times) / 16k

→ Average = (16k * 20) / 16k

→ Average = 20..

Now, given that, 11k of the numbers are doubled..

Than, 11k terms becomes 40 each.

So,

→ sum of numbers = (40 + 40 + _________ 11k times)

→ sum of numbers = 11k * 40 = 11000 * 40 = 440000 .

Now, given that, remaining 5k of the numbers are tripled..

Than, 5k terms becomes 60 each.

So,

→ sum of numbers = (60 + 60 + _________ 5k times)

→ sum of numbers = 5k * 60 = 5000 * 60 = 300000 .

Therefore,

→ sum of all 16k new numbers = 440000 + 300000 = 740000

Hence,

→ New Average of 16k numbers = (740000) / (16000) = 46.25 .

So,

→ New Average increased by = 46.25 - 20 = 26.25 .

Hence,

→ % increased = (26.25 * 100) / 20 = 131.25 . (Ans.)