Practice Exercise:
Averages |
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Assume two groups with Averages A_{1}, A_{2} and number of members n_{1} and n_{2}. Then the weighted average of the groups Aw is:
A_{w} = ( n_{1} * A_{1} + n_{2} * A_{2} ) / ( n_{1} + n_{2 })
n_{1 }* A_{w} + n_{2} * A_{w} = n_{1} * A_{1} + n_{2} * A_{2}
n_{1} ( A_{w - }A_{1} ) = n_{2 }( A_{2} - A_{w})
n_{1} / n_{2} = ( A_{2} - A_{w}) / ( A_{w - }A_{1} )
Note: For convenience when two averages are given we taken smaller value as A_{1} and other value as A_{2}.
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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