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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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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