Difficult Bar Charts Solved QuestionData Interpretation Discussion

Common Information

The residents of a city ‘$X$’ consume only two varieties of rice viz. ‘High Quality’ and ‘Low Quality’.

The following bar - graph provides information about the percentage change in the consumption of the two varieties of rice by the residents of the city ‘$X$’ compared to the previous year for the years $2003$ to $2008$.

The consumption of ‘High Quality’ rice by the residents of the city ‘$X$’ in the year $2002$ was more than that of ‘Low Quality’ rice.

 Q. Common Information Question: 2/3 In which of the given years from $2003$ to $2008$, the total consumption of rice by the residents of city ‘$X$’ was the maximum?
 ✖ A. 2007 ✖ B. 2008 ✖ C. 2006 ✔ D. 2003 ✖ E. Cannot be determined

Solution:
Option(D) is correct

Let the consumption of ‘High Quality’ and ‘Low Quality’ rice by the residents of the city X in the year 2002 be ‘A’ and ‘B’ respectively. It is given that A>B

Table below can be scrolled horizontally

2002 2003 2004 2005 2006 2007 2008

A

1.2A

0.3A

0.15A

0.18A

0.225A

0.09A

B

0.8B

0.6B

0.84B

0.21B

0.126B

0.189B

As $A$ and $B$ are positive quantities, it is very clear that the consumption of ‘High Quality’ rice is maximum in the year $2003$ and the consumption of ‘Low Quality’ rice is 2nd highest in $2003$ (it is highest in the year $2005$).

Total consumption of rice in the year $2003$ is definitely more than that of each of the years $2004, 2006, 2007$ and $2008$.

We need to compare the data for the years $2003$ and $2005$.

Let the total consumption of rice in the years $2003$ and $2005$ be $x$ and $y$ respectively.

We know that $x=1.2A + 0.8B$ and

$y = 0.15A + 0.84B$

$x - y = 1.05A - 0.04B$

Now, As $A > B$, $1.05A > 1.05B > 0.04B$

$⇒ 1.05A > 0.04B$or $1.05A - 0.04B > 0$

$⇒ x - y > 0$ or, $x > y$.

⇒ The total consumption of rice in the year $2003$ is the maximum in the period $2003-2008$.