Data 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. |
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 |

**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.