The given pie chart shows the annual agricultural yield of a certain place. If the total production is 8100 tons and the yield of sugarcane in a different year was 2400 tons, find the yield of rice in both years?

Hint: We start solving the problem by finding the proportions of the yield of sugarcane and rice in the total annual production. This can be done by dividing the given angle corresponding to each crop by ${{360}^{\circ}}$ which is the total angle at the centre of the circle. We then find the yield of sugarcane and rice using the proportions we just obtained. We then find the relation between the yield of sugarcane and rice. We then find the yield of rice in different years using this year.

Complete step by step answer:
According to the problem, we are given a pie chart showing the annual agricultural yield of a certain place. We need to find the yield of two years if the total production is 8100 tons and the yield of sugarcane in a different year was 2400 tons.
Let us find the proportions of sugarcane and rice productions in total annual production.
We know that the proportion can be calculated by taking the ratio of the angle of part of the crop to ${{360}^{\circ }}$.
So, we get proportion of sugarcane in total annual production as $\dfrac{{{80}^{\circ }}}{{{360}^{\circ }}}=\dfrac{2}{9}$.
Now, the proportion of rice in total annual production as $\dfrac{{{40}^{\circ }}}{{{360}^{\circ }}}=\dfrac{1}{9}$.
According to the problem, we are given that the total annual production of this year is 8100 tons.
Using the proportion of sugarcane, we get the annual production of sugarcane as $\dfrac{2}{9}\times 8100=1800$ tons.
Similarly, we get the annual production of rice as $\dfrac{1}{9}\times 8100=900$ tons.
We can see that the annual production of rice is half of the annual production of sugarcane.
According to the problem, we are given that production of sugarcane on a different year was 2400 tons.
We get the production of rice in that year as $\dfrac{1}{2}\times 2400=1200$ tons.
So, we have found yield of rice in both years as 900 tons and 1200 tons.

Note:
We should make sure that the annual production is equal to the sum of the annual production of all the crops given in the pie chart. We have taken the assumption that the pie chart is valid for that year where the production of sugarcane is given as 2400 tons. We can also find the total production of that year where the production of sugarcane was given as 2400 tons. Similarly, we can expect problems to find the yield of other crops given in the pie chart.