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. |
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 $2003-2008$.