Bar Charts
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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.

Common information image for Bar Charts, Data Interpretation:1171-1

Q.

Common Information Question: 3/3

The total consumption of rice by the residents of city ‘$X$’ in $2006$ was not less than $50%$ of that in the year $2004$.

In which of the following years, the consumption of ‘High Quality’ rice was not necessarily more than that of ‘Low Quality’ rice?

 A.

2008

 B.

2006

 C.

2004

 D.

2007

 E.

2005

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Solution:
Option(E) 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

Total consumption of rice by the residents of city $X$ in $2004$:

$= 0.3A + 0.6B$

Total consumption of rice by the residents of city $X$ in $2006$:

$= 0.18A + 0.21B$

$⇒ 18A + 21B ≥ \dfrac{1}{2} (30A + 60B)$

$⇒ 6A ≥ 18B$

$⇒ A ≥ 3B$

Except for the year $2005$, in each of the years in the period $2003 - 2008$, the consumption ‘High Quality’ rice is definitely more than that of ‘Low Quality’ rice.


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