Average of ten positive numbers is X. If each number is increased by 10%, then new average increases by:
- AOption (a)
10%
- BOption (b)
11%
- COption (c)
12%
- DOption (d)
8%
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Correct answer
10%
Why this answer is correct
Shortcut Trick
If each observation in a data set is increased by p%, the average of that data set also increases by p%.
Initial Average = X
Each number is increased by 10%.
Increase in Average = 10% of X = 0.1X
The new average increases by a factor of 0.1.
∴ The correct option is A.
Alternate Method
Given:
Number of observations (n) = 10
Initial Average = X
Formula: Average = Sum of observations ÷ Total number of observations
Initial Average (X)
New Average (1.1X)
Increase = 10% of X = 0.1X
⇒ Sum of 10 numbers = 10 × X = 10X
⇒ Each number is increased by 10%.
⇒ New value of each number = original + 0.1 × original = 1.1 × original
⇒ New Sum = 1.1 × (Sum of 10 numbers) = 1.1 × 10X = 11X
⇒ New Average = New Sum ÷ 10
⇒ New Average = 11X ÷ 10 = 1.1X
⇒ Increase in average = New Average − Old Average
⇒ Increase = 1.1X − X = 0.1X
∴ The correct option is A.
Additional Information
Addition/Subtraction Rule
If a constant 'k' is added to or subtracted from each term, the new average becomes (Original Average ± k).
Multiplication/Division Rule
If each term is multiplied or divided by a constant 'k', the new average becomes (Original Average × k) or (Original Average ÷ k).
Percentage Change in Average
If each number is changed by p%, the average changes by the same p% because of the linear property of the sum.