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Average of x numbers is 82. When two more numbers are added to these x numbers, then the average of all numbers becomes 80. When the same two numbers are subtracted from the sum of x numbers, then the average of remaining numbers becomes 85. Find sum of x numbers.
  • a)
    1640
  • b)
    1230
  • c)
    738
  • d)
    820
  • e)
    1312
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Average of x numbers is 82. When two more numbers are added to these ...
Let sum of x numbers = y
So y/x = 82, y = 82x
Let sum of two numbers added = z
So, (y+z)/(x+2) = 80
Y+z = 80x +160 .... (1)
And when these are subtracted
Then (y-z)/(x-2) = 85
y-z = 85x -170 .....(2)
by solving equation 1 and 2, we get
2y = 165x-10
165x-2y = 10
165x-164x = 10
X = 10 numbers
Hence, sum of x numbers = 82×10 = 820
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