What is the total food grain production in 2002 given the following conditions?

Question

The production of rice in the year $2001$ was $1000$ tonnes which was $25$% of the total food grains production in that year.In the next year ,if the production of rice is decreased by $4$%. and the production of rice as the percentage of total food grain production increased by $5$ percentage points.What is the total food grain production in $2002$?

MyApproach

Production of rice in the year $2001$ was $1000$

Percentage with respect of total food grain in $2001$ was $25$%.

Production of rice in the year $2002$ was $960$(as it is decreased by $4%$)

Percentage with respect of total food grain in $2002$ was $30$%.

I am not able to relate the equations and calculate the total food grain production in $2002$.

Can Anyone guide me how to solve the problem?

Answer 1

Let $TFGP_y$ be the Total Food Grain Production in year $y$.

Then we have $25$% of $TFGP_{2001}=1000$ so $\dfrac14TGFP_{2001}=1000\implies TGFP_{2001}=4000$.

In $2002$, the equation becomes $\dfrac3{10}TGFP_{2002}=960$, so $TGFP_{2002}=3200$.

Answer 2

In 2002 the production of rice was 960, which corresponds to $30\%$ of the total food grains production $. \quad \checkmark$

Now you have to calculate how many tons correspond to $100\%$.

$30\% \ \widehat = \ 960$

$100\% \ \widehat = \ x $

Apply the rule of three to calculate x.

You start with $x=960\cdot \large{\frac{\cdots}{\cdots}}\ $,

where $960$ is the base value. Next you build a fraction from the two remaining numbers $30\%$ and $100\%$. The percent sign can be omitted since it is cancelled out. The more of the total food grains production in year 2001, the more rice production in year 2001 we have. Thus 960 has to increase and therefore the fraction as to be $\textrm{greater than 1}$. Thus we have the calculation

$$x=960\cdot \frac{100}{30}=960\cdot \frac{10}{3}=320\cdot \frac{10}{1}=3200$$