Sanjay wrote 25 consecutive even natural numbers on the board. The average of these numbers is A and largest number is X. After erasing one of the numbers, the average become B. He replaced the erased number with (X + 2) and the average become C. Find the difference between A and C if it is known that B is 59.5.
Sanjay wrote 25 consecutive even natural numbers on the board. The average of these numbers is A and largest number is X. After erasing one of the numbers, the average become B. He replaced the erased number with (X + 2) and the average become C. Find the difference between A and C if it is known that B is 59.5.
Option 1 -
0.56
Option 2 -
0.5
Option 3 -
1.06
Option 4 -
1
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1 Answer
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Correct Option - 1
Detailed Solution:It is given average of 24 numbers = 59.5
Sum = 59.5 ×24 = 1428
Let the numbers erased be ‘m’
1428 + m =
1428 + m = 50n + 650
50n – m = 778
Least value ‘n’ can take 16
(i) for n = 16, m =22
Series 2 (17, 18… 41)
i.e. 34, 36, 38 ….82
from this series we cannot remove 22. So, this case is not valid.
(ii) for n = 17, m = 72
Series 2 (18, 19… 42)
Only this case is valid
Average (A) = = 60
Sum of series after removing 72 and adding next consecutive even number
1500 – 72 + 86 = 1514
Average (C) = 1514/25 = 60.56
A – C = 60 – 60.56
= 0.56
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