Question : Directions: A health drink company prepares the drink in three flavours: P, Q, and R. The production of three flavours over six years has been expressed on a bar graph below. Study the graph and answer the question. Production of 3 different flavours of health drinks by the company in 6 years (in lakh bottles):

Which of the following years is the percentage rise or fall in production from the previous year the maximum for the flavour Q?

Option 1: 2007

Option 2: 2009

Option 3: 2010

Option 4: 2006

Correct Answer: 2007

Solution : For the year 2006,
Production of flavour Q in 2006 = 60 lakh
Production of flavour Q in 2005 = 55 lakh
Percentage change = $\frac{\text{Production of flavour Q in 2006 – Production of flavour Q in 2007}}{\text{Production of flavour Q in 2005}}$ × 100
Percentage change = $\frac{60- 55}{55}$ × 100 = 9.09% (increase)
For the year 2007,
Production of flavour Q in 2007 = 50 lakh
Production of flavour Q in 2006 = 60 lakh
Percentage change = $\frac{\text{Production of flavour Q in 2006 – Production of flavour Q in 2007}}{\text{Production of flavour Q in 2006}}$ × 100
Percentage Change = $\frac{60–50}{60}$ × 100 = 16.66% (decrease)
For the year 2008,
Production of flavour Q in 2007 = 50 lakh
Production of flavour Q in 2008 = 55 lakh
Percentage change = $\frac{\text{Production of flavour Q in 2008 – Production of flavour Q in 2007}}{\text{Production of flavour Q in 2007}}$ × 100
Percentage change = $\frac{55–50}{50}$ × 100 = 10% (increase)
For the year 2009,
Production of flavour Q in 2009 = 50 lakh
Production of flavour Q in 2008 = 55 lakh
Percentage change = $\frac{\text{Production of flavour Q in 2008 – Production of flavour Q in 2009}}{\text{Production of flavour Q in 2008}}$ × 100
Percentage change = $\frac{55–50}{55}$ × 100 = 9.09% (decrease)
For the year 2010,
Production of flavour Q in 2009 = 50 lakh
Production of flavour Q in 2010 = 55 lakh
Percentage change = $\frac{\text{Production of flavour Q in 2010–Production of flavour Q in 2009}}{\text{Production of flavour Q in 2009}}$ × 100
Percentage change = $\frac{55–50}{50}$ × 100 = 10% (increase)
The maximum change is the rise/fall in production from the previous year was 16.67% during 2007.
Hence, the correct answer is 2007.