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The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first added is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
  • a)
    40.4
  • b)
    40.2
  • c)
    43.8
  • d)
    42.4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The average of 10 numbers is 40.2. Later it is found that two numbers ...
Sum of 10 numbers = 10 * 40.2 = 402
1st number added is 18 more than actual number, So, 18 must be subtracted
Also, 2nd number added is 13 instead of 31, So, 13 should be subtracted and 31 should be added
=> Actual sum of 10 numbers = 402 – 18 – 13 + 31 = 402
=> Actual average = 402 / 10 = 40.2
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Most Upvoted Answer
The average of 10 numbers is 40.2. Later it is found that two numbers ...
Given:
- Average of 10 numbers = 40.2

To find:
- Correct average after two numbers have been wrongly copied

Solution:

Step 1:
Let's assume the sum of 10 numbers is x
- Therefore, the average of 10 numbers = x/10

Step 2:
According to the question, two numbers have been wrongly copied
- The first number added is 18 greater than the actual number
- The second number added is 18 less than the actual number

Step 3:
Let's assume the actual sum of 10 numbers is y
- Therefore, y = sum of 10 numbers - (18 - 13) = x - 5

Step 4:
Let's assume the actual value of the first wrongly copied number is a
- Therefore, a - 18 is the actual value of that number
- Similarly, let's assume the actual value of the second wrongly copied number is b
- Therefore, b + 18 is the actual value of that number

Step 5:
Now, we can write the equation:
- (sum of 10 numbers - (wrongly copied number 1) - (wrongly copied number 2) + (actual value of wrongly copied number 1) + (actual value of wrongly copied number 2))/10 = correct average

Step 6:
Substituting the values, we get:
- (x - 18 - 13 + (a - 18) + (b + 18))/10 = correct average
- (x - (13 + 18) + (a + b))/10 = correct average
- (x - 31 + (a + b))/10 = correct average

Step 7:
Substituting the given value of average in the above equation, we get:
- (x - 31 + (a + b))/10 = 40.2

Step 8:
Substituting the value of y in the above equation, we get:
- (y + (a + b))/10 = 40.2
- (x - 5 + (a + b))/10 = 40.2
- (x + a + b - 5)/10 = 40.2
- x + a + b = 407

Step 9:
Substituting the value of x in the above equation, we get:
- y + a + b - 5 = 407
- y + a + b = 412

Step 10:
Substituting the value of y + a + b in the equation of correct average, we get:
- correct average = (y + a + b)/10
- correct average = 412/10
- correct average = 41.2

Therefore, the correct average after two numbers have been wrongly copied is 41.2.

Answer:
- Option B) 40.2
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The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first added is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.a)40.4b)40.2c)43.8d)42.4Correct answer is option 'B'. Can you explain this answer?
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