Question

A mixture contains rice, flour, corn in the ratio of $5:9:2$. If the mixture weighs $800$ grams, find the percentage of rice, flour, corn in the mixture.

Answer 1

Hint:
Add the ratio to get the whole. Use this as a denominator and each ratio term becomes a numerator. Convert the ratio into fractions. Then multiply the fraction by $100$ it becomes percentage.

Complete step by step solution:
Since the ratio of the mixture of rice, flour, corn is $5:9:2$. If we want to find the percentage of the mixture we have to make it as a fraction, for that we have to add the ratio.
Sum of the ratio = $5+9+2=16$ , take it as a denominator.
Now we have to find the percentage of rice,
$\Rightarrow $ So take the ratio term of rice as a numerator that is $5$ and the denominator is $16$ so we get the fraction as $\dfrac{5}{16}$now we have to multiply this fraction by $100$.
$\Rightarrow $ Percentage of rice = $\dfrac{5}{16}\times 100$
If we divide the fraction we get,
$\Rightarrow $ Percentage of rice = $0.3125\times 100$
$\Rightarrow $ Percentage of rice =$31.25$%
Now we have to find the percentage of flour,
$\Rightarrow $ So take the ratio term of flour as a numerator so we get the fraction as $\dfrac{9}{16}$now we have to multiply this fraction by $100$.
$\Rightarrow $ Percentage of flour= $\dfrac{9}{16}\times 100$
If we divide the fraction we get,
$\Rightarrow $ Percentage of flour= $0.5625\times 100$
$\Rightarrow $ Percentage of flour =$56.25$%
Now we have to find the percentage of corn,
$\Rightarrow $ So take the ratio term of corn as a numerator so we get the fraction as $\dfrac{2}{16}$now we have to multiply this fraction by $100$.
$\Rightarrow $ Percentage of corn = $\dfrac{2}{16}\times 100$
If we divide the fraction we get,
$\Rightarrow $ Percentage of corn= $0.125\times 100$
$\Rightarrow $ Percentage of corn =$12.5$%

Percentage of rice, flour, corn is $31.25$%, $56.25$%, $12.5$%.

Note:
The mixture weighs $800$ grams. From that we can additionally calculate the weight of each term. For that we can convert the percentage into fraction and multiply the fraction by the weight of the mixture,
$\Rightarrow $ Weight of rice = percentage of rice × $800$
To convert percentage into fraction writes the percent divided by $100$
$\Rightarrow $ Weight of rice = $31.25$% ×$800$
$\Rightarrow $ Weight of rice = $\dfrac{31.25}{100}\times 800$
Cancelling we get,
$\Rightarrow $ Weight of rice = $31.25\times 8$
$\Rightarrow $ Weight of rice = $450$grams.
Now we have to find the weight of flour
$\Rightarrow $ Weight of flour = percentage of flour × $800$
$\Rightarrow $ Weight of flour = $56.25%\times 800$
$\Rightarrow $ Weight of flour = $\dfrac{56.25}{100}\times 800$
Cancelling we get,
$\Rightarrow $ Weight of flour = $56.25\times 8$
$\Rightarrow $ Weight of flour = $250$grams.
Now we have to find the weight of corn
$\Rightarrow $ Weight of corn = percentage of corn × $800$
$\Rightarrow $ Weight of corn = $12.5$% ×$800$
$\Rightarrow $ Weight of corn = $\dfrac{12.5}{100}\times 800$
Cancelling we get,
$\Rightarrow $ Weight of corn = $12.5$×$8$
$\Rightarrow $ Weight of corn = $100$grams.