the average of 20 no.s is 40. if the 11th no. is doubled and 5 is subtracted from each other expect the 11th then the new average is 50. what is the value of 11th no.?
Answers
Answer:
Mean=20
Total numbers=10
Total sum=200
If 5 is decreased from all numbers
mean subtracting (10×5) from 200 make total sum=200−50=150
New Mean=
10
150
=15
Hence New Mean =15
Answer:
The value of the 11th no. in the given list is 82.5
Step-by-step explanation:
Let's assume that the 11th number in the given sequence is 'x'.
According to the probl em statement, the average of 20 numbers is 40. This means that the sum of all the 20 numbers is (20 x 40) = 800.
We know that the new average is 50 after doubling the 11th number and subtracting 5 from each of the oth er 19 numbers. This means that the sum of all the 20 numbers after these operations is (20 x 50) = 1000.
Let's now use these two equations to solve for 'x', which is the 11th number:
(1) Sum of 20 numbers = (20 x 40) = 800
(2) Sum of 20 numbers after operations = (20 x 50) = 1000
We know that in the second equation, the 11th number 'x' is doubled and then 5 is subtracted from each of the other 19 numbers. This means that the sum of the original 20 numbers (before the operations) is (1000 + 5 x 19 - 2x) = (965 - 2x).
Now we can equate the sum of the original 20 numbers from equation (1) and (2) to solve for 'x':
800 = 965 - 2x
2x = 165
x = 82.5
Therefore, the 11th number in the sequence is
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