Question

A farmer produced $1\dfrac{3}{5}$ times as much as peanuts this season as he did last season . What is the ratio of last season production as compared to this season ?

Answer 1

Hint:First Let us take the $x$ will be the production of peanuts in the last season and they given he produces $1\dfrac{3}{5}$ as much as peanuts in this year production , Hence this year production is $\dfrac{8}{5}x$.We have to find the ratio of last season production as compared to this season that is equal to =$\dfrac{{{\text{Last year production }}}}{{{\text{This year production}}}}$.

Complete step-by-step answer:
As in the question it is given that the farmer will produce $1\dfrac{3}{5}$ times as much as peanuts that he produced last year .
We convert mixed fraction into improper fraction
$1\dfrac{3}{5}$ as $\dfrac{{5 \times 1 + 3}}{5} = \dfrac{8}{5}$ ;
So for this , Let us take the $x$ will be the production of peanuts in the last season ,
Hence in the question it is given that he will produce $\dfrac{8}{5}$ times more in this season ,
So if the last year the production is $x$ then this year production will be $\dfrac{8}{5}x$
Now , we have to find the ratio of last season production as compared to this season that is equal to =$\dfrac{{{\text{Last year production }}}}{{{\text{This year production}}}}$

Last year production = $x$ This year production = $\dfrac{8}{5}x$
Ratio = $\dfrac{x}{{\dfrac{8}{5}x}}$ or $\dfrac{x}{{\dfrac{{8x}}{5}}}$
Hence $x$ is common in both numerator and denominator hence it will cancel out ,
$\dfrac{1}{{\dfrac{8}{5}}}$
Now $5$ will transfer to numerator because it is like $1 \div \dfrac{8}{5}$ now its solution is $1 \times \dfrac{5}{8}$
Hence the ratio last season production as compared to this season is $\dfrac{5}{8}$ or $5:8$

Note:A proportion in which the consequent of each ratio is the antecedent of the next (as 2:4=4:16=16:32) is known as continued proportion.Consider two ratios to be a: b and c: d.Then in order to find the continued proportion for the two given ratio terms, we convert the mean into a single term. For this we would take the LCM of means.For the given ratio, the LCM of b & c will be bc.Thus, multiplying the first ratio by c and second ratio by b, we have,
First ratio- ca : bc
Second ratio- bc : bd
Thus, the continued proportion can be written in the form of ca: bc: bd