The percentage rise/fall in production from the previous year for flavor Y during various years are:
In 2006 = 60 - \(\frac{55}{55}\)\(\times\) 100 = 9.09 \(\%\) increase
In 2007 = 60 - \(\frac{50}{60}\)\(\times\) 100 = 16.67\(\%\) decrease
In 2008 = 55 - \(\frac{50}{50}\)\(\times\)100 = 10\(\%\) increase
In 2009 = 55 - \(\frac{50}{50}\)\(\times\)100 = 9.09\(\%\) decrease
In 2010 = 55 - \(\frac{50}{50}\)\(\times\) 100 = 10\(\%\) increase
Therefore, Maximum change is decrease of 16.67\(\%\) during 2007.So the correct option is (A)
Average annual productions over the given period for various flavours are:
For Flavour X = [\(\frac{1}{6}\times\)(50+40+55+45+60+50)] = 50 lakh
For Flavour Y = [\(\frac{1}{6}\times\)(55+60+55+50+50+55)] = 54.17
lakh For flavour Z = [\(\frac{1}{6}\times\)(45+50+60+60+45+40)= 50 lakh
Maximum average production is for Flavour Y.So the correct option is (B)
Average production of flavour X in 2005, 2006 and 2007 =
\(\frac{1}{3}\times\)(50+40+55)
\(=\frac{145}{3}\) lakh
Average production of flavour Y in 2008, 2009 and 2010 =
\(\frac{1}{3}\times\)(55+50+55)
\(=\frac{160}{3}\)lakh
Difference \(=\frac{160}{3}-\frac{145}{3}=\frac{15}{3}\)
= 5 lakh
= 500000.
So the correct option is (A)