Question

Gunpowder contains $75\% $of nitre and $10\% $of Sulphur. Find the amount of gunpowder which carries $9kg$ nitre. What amount of gunpowder would contain $2.5kg$ sulphur?

Answer 1

Hint: First, convert the kilograms into grams so that it is easy to calculate, and after getting the final answer again convert the grams into the kilogram to get the required resultant.
The percentage concept is used in the given problem, which is the number or the given ratio is represented in the form of fractions with $100$.
The percentage is represented in the sign $\% $.
Like in $70\% $ of $40$ is $28$ where, $70\% $ is the given percent, $40$ is the base, and $28$ is the part value.

Complete step by step answer:
Since from the given that the gunpowder amount is $9kg$ and converts into the grams using the kilograms to grams converting that $1kg = 1000g$
Thus, we get, for $9kg$ we get $9kg = 9000g$
We need to find in what grams of the gunpowder carry the given $9000g$
Now the gunpowder contains the $75\% $of nitre, and x is the unknown gram, by the use of percentage concept we can convert that into, $75\% $of $x = 9000$
$\dfrac{{75}}{{100}} \times x = 9000$$ \Rightarrow x = \dfrac{{9000 \times 100}}{{75}}$
Thus, we get, $x = 12000g$ and this can be again converted into $12000g = 12kg$
Hence, $12kg$ gunpowder carries $9kg$ nitre.
Now for the quantity of Sulphur in the gunpowder is given us, $10\% $of Sulphur.
Assume $y$ be the kilogram of gunpowder containing $2.5kg$ sulphur.
Which is $10\% $ of $y = 2.5kg$
$ \Rightarrow \dfrac{{10}}{{100}}y = 2500g$
$ \Rightarrow y = \dfrac{{2500 \times 100}}{{10}} = 25000g$
Converting into the kilogram we get, $25000g \Rightarrow 25kg$
Hence the quantity of gunpowder is $25kg$carried $2.5kg$sulphur.

Note: Since the kilogram can be converted into the grams as $1kg = 1000g$and similarly, we can also able to convert the grams into kilograms with the help of division operation that, $1g = \dfrac{1}{{1000}}kg$
We are also able to solve the problem without converting the kilograms to grams as we get the same results only.
Like, $75\% $of $x = 9kg$$\dfrac{{75}}{{100}} \times x = 9$$ \Rightarrow x = \dfrac{{9 \times 100}}{{75}}$$ \Rightarrow x = 12kg$
Hence, $12kg$ gunpowder carries $9kg$ nitre.
And for $10\% $of $y = 2.5kg$$ \Rightarrow \dfrac{{10}}{{100}}y = 2.5kg$$ \Rightarrow y = \dfrac{{2.5 \times 100}}{{10}} = 25kg$
Thus, the quantity of the gunpowder is $25kg$ which contains $2.5kg$ sulphur.