Average of ten positive numbers is x. If each number increases by 10%, then x-
Solution
Correct Answer: Option D
Let, the ten positive numbers are n1 + n2 + n3 + ........... + n10
Then, n1 + n2 + n3 + ........... + n10 = X ............(1)
According to the question,
each number is increased by 10%
10% = 10/100 = 0.1
Suppose, the average of the ten numbers = X1
Therefore, X1 =( 1.1n1 + 1.1n2 + 1.1n3 + ........... + 1.1n10)/10
⇒ X1 = 1.1(n1 + n2 + n3 + ........... + n10)/10
⇒ X1 = 1.1X [We get from equation (1)]
⇒ X1/ X = 1.1
⇒ X1/X = (1.1 x 100)%
⇒ X1/X = 110%
Total percentage gains = (110 - 100)% = 10%
∴ The new average increases by 10%
Then, n1 + n2 + n3 + ........... + n10 = X ............(1)
According to the question,
each number is increased by 10%
10% = 10/100 = 0.1
Suppose, the average of the ten numbers = X1
Therefore, X1 =( 1.1n1 + 1.1n2 + 1.1n3 + ........... + 1.1n10)/10
⇒ X1 = 1.1(n1 + n2 + n3 + ........... + n10)/10
⇒ X1 = 1.1X [We get from equation (1)]
⇒ X1/ X = 1.1
⇒ X1/X = (1.1 x 100)%
⇒ X1/X = 110%
Total percentage gains = (110 - 100)% = 10%
∴ The new average increases by 10%
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