Practice Exercise:
Averages |
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Assume two groups with Averages A1, A2 and number of members n1 and n2. Then the weighted average of the groups Aw is:
Aw = ( n1 * A1 + n2 * A2 ) / ( n1 + n2 )
n1 * Aw + n2 * Aw = n1 * A1 + n2 * A2
n1 ( Aw - A1 ) = n2 ( A2 - Aw)
n1 / n2 = ( A2 - Aw) / ( Aw - A1 )
Note: For convenience when two averages are given we taken smaller value as A1 and other value as A2.
Practice Exercise:
Alligations |
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Calculate Absolute value change or percentage change:
If sales of a year is Rs. 1000 and next year is Rs. 2000 then the absolute value change is Rs. 1000 and the percentage change is:
%change = (Absolute value change) * 100 / Original quantity
Calculate percentage change and percentage point change:
If earlier Yes bank offered 6% interest rate on savings and now offers 4% interest. Then calculate percentage change and percentage point change.
%point change = 6 - 4 = 2%
%change in savings rate = (6 - 4) / 2 * 100 = 100% reduction.
Effect of percentage change on a ratio:
The ratio has a relation with the numerator, when numerator increases the ratio increases. Thus increase in the numerator only keeping the denominator constant will increase the ratio.
11 / 17 is 10% more than 10 / 17.
Calculation of successive percentage changes:
A's salary increases by 20% and then decreases by 20%. What is the net percentage change in salary of A.
To calculate this we assume A's initial salary is 100 which increases by 20% so ( + 20 ) and then becomes 120. Then it decreases by 20% so becomes 96 (-24). Hence net change is +20 - 24 = -4% change or 4% decrease.
A trader gives successive discounts of 10, 20, 10% find the net percentage change.
To calculate this we should assume original price as 100. Then 10% discount makes it 90 (-10), 20% discount on 90 is 72 (-18) and then 10% discount on 72 is 64.8 (-7.2) so net change is = -10-18-7.2 = -35.2 or 35.2% reduction.
Practice Exercise:
Percentage |
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