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The average of 10 numbers is 20. If a number equal in value to the largest of the 10 given numbers is added to the given set, the average increases by 1. But instead of adding the number, if the largest number itself is deleted, then what will be the average?
  • a)
    16.66
  • b)
    18.77
  • c)
    20.01
  • d)
    20.33
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The average of 10 numbers is 20. If a number equal in value to the lar...
Sum of 10 numbers = 200
Assume that x is the maximum.
If x is deleted, average
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Community Answer
The average of 10 numbers is 20. If a number equal in value to the lar...
Given Information:

- There are 10 numbers.
- The average of these 10 numbers is 20.

Adding the largest number:

- Let's assume the largest number in the given set is 'x'.
- If we add 'x' to the given set, the total sum of the numbers would increase by 'x'.
- The new sum of the 11 numbers would be the sum of the original 10 numbers plus 'x'.
- The new average would be the new sum divided by 11.
- It is given that the new average is 1 more than the original average, which means the new average is 21.
- So, we have the equation: (sum of the original 10 numbers + x) / 11 = 21.

Finding the value of 'x':

- We know that the average of the original 10 numbers is 20, so the sum of the original 10 numbers is 20 multiplied by 10, which is 200.
- Substituting this value in the equation, we have: (200 + x) / 11 = 21.
- Solving this equation, we get: 200 + x = 231.
- Therefore, x = 231 - 200 = 31.

Deleting the largest number:

- If we delete the largest number from the given set, the total sum of the remaining 9 numbers would decrease by 31.
- The new sum would be the sum of the original 10 numbers minus 31.
- The new average would be the new sum divided by 9.
- So, the new average would be (200 - 31) / 9 = 169 / 9 = 18.77.

Conclusion:

- Therefore, if instead of adding the largest number, we delete it, the new average would be 18.77.
- Hence, the correct answer is option 'B' - 18.77.
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The average of 10 numbers is 20. If a number equal in value to the largest of the 10 given numbers is added to the given set, the average increases by 1. But instead of adding the number, if the largest number itself is deleted, then what will be the average?a)16.66b)18.77c)20.01d)20.33Correct answer is option 'B'. Can you explain this answer?
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