The following line graph shows the ratio of wheat production to rice production of a state in India over 7 years, from 1999 to 2006. Answer the question based on this data.
If the rice production in 2003 was 4 lac tons, what was its wheat production during 2003?
Show Hint
Multiply the rice production by the wheat-to-rice ratio read off the graph for that year.
Instead of multiplying directly, this can be solved by setting up a proportion, which helps when a ratio is given as "wheat : rice" rather than as a plain decimal.
From the graph, for the year 2003, wheat : rice $= 1.2 : 1$, which is the same as $6:5$ (multiplying both parts by 5).
Let the wheat production be $w$ lac tons. Since rice production is 4 lac tons, and the ratio of wheat to rice is $6:5$:
\[ \frac{w}{4} = \frac{6}{5} \]
Cross multiplying:
\[ 5w = 24 \Rightarrow w = 4.8 \]
Let's summarize:
The wheat to rice ratio for 2003 read off the graph is 1.2, equivalent to 6:5.
Applying this ratio to the known rice production of 4 lac tons gives a wheat production of 4.8 lac tons.
So the wheat production in 2003 was 4.8 lac tons, matching option (C).
