CA Foundation doubt
If 5 subtracted from each observation of some certain item then its co-efficient of variation is 10% and if 5 is added to each item then its coefficient of variation is 6%. Find original coefficient of variation. Anyone can solve this question.
Asked by Ajay23 Apr 2024749 views
Ajay Β· 24 Apr 2024
Thank you..
Aneri Β· 23 Apr 2024
For coefficient of variation = 10% alpha/(x + 5) * 100 = 10 (Equation 1) For coefficient of variation = 6% alpha/(x - 5) * 100 = 6 (Equation 2) Now, Divide Equation 1 and Equation 2, We get, (x + 5)/(x - 5) = 10/6 (x + 5)/(x - 5) = 5/3 .. 3x + 15 = 5x - 25 .. 5x - 3x = 15 + 25 put x = 20 in equation 1 alpha/(20 - 5) * 100 = 10 alpha = (10 * 15)/100 .. 2x = 40 .. x = 20 Now, alpha = 1.5
Aneri Β· 23 Apr 2024
View attached PDFAneri Β· 23 Apr 2024
For coefficient of variation = 10% β π₯ + 5 β 100 = 10 x+5 β β β100=10 .............................. (Equation 1) For coefficient of variation = 6% β π₯ β 5 β 100 = 6 xβ5 β β β100=6 ................................. (Equation 2) Now, Divide Equation 1 and Equation 2, We get, β΄ π₯ + 5 π₯ β 5 = 10 6 xβ5 x+5 β = 6 10 β β΄ π₯ + 5 π₯ β 5 = 5 3 xβ5 x+5 β = 3 5 β β΄ 3x + 15 = 5x - 25 β΄ 5x - 3x = 15 + 25 β΄ 2x = 40 β΄ x = 20 Now, put x = 20 in equation 1 β 20 β 5 β 100 = 10 20β5 β β β100=10 β = 10 β 15 100 100 10β15 β β = 1.5 Now, Coefficient of variation is 1.5 20 β 100 20 1.5 β β100 = 7.5 β΄ Coefficient of variation is 7.5%
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