Question

1. Chalk contains calcium, carbon and oxygen in the ratio of \[10:3:12\]. Find the percentage of carbon in chalk.
2. If in a stick of chalk carbon is 3g, what is the weight of the chalk stick?

Answer 1

Hint: In problem 1, we have to find the percentage of carbon in chalk if Chalk contains calcium, carbon and oxygen in the ratio of \[10:3:12\]. We can first find the total parts and use the formula \[Percentage=\dfrac{\text{Parts of carbon}}{\text{Total parts}}\times 100\] to find the percentage and in problem 2, we have to find the weight of chalk stick if carbon is 3g in it. We know that there will be 12 percent of carbon from problem 1, using the formula \[\text{Weight of carbon}=percent\times \text{weight of chalk}\] and find the weight of it.

Complete step by step solution:
Problem 1:
Here we have to find the percentage of carbon in chalk if Chalk contains calcium, carbon and oxygen in the ratio of \[10:3:12\].
We can now write the total parts,
Total parts = 10 + 3 + 12 = 25 ……… (1)
We know that parts of carbon given in the ratio is 3.
We can now substitute these in the formula \[Percentage=\dfrac{\text{Parts of carbon}}{\text{Total parts}}\times 100\], we get
\[\Rightarrow Percentage=\dfrac{3}{25}\times 100=12\]
Therefore, there will be\[12\%\] of carbon in chalk.
Problem 2:
Here we have to find the weight of the chalk stick if carbon is 3g in it.
We know that there will be 12 percent of carbon from problem 1.
We can now use the formula \[\text{Weight of carbon}=percent\times \text{weight of chalk}\].
\[\begin{align}
  & \Rightarrow 3=12\%\times \text{weight of chalk} \\
 & \Rightarrow \text{Weight of chalk = }\dfrac{100}{12}\times 3=25 \\
\end{align}\]
Therefore, the weight of the chalk is 25g.

Note: We should always remember that to find the percentage, we can use the formula \[Percentage=\dfrac{\text{Parts of carbon}}{\text{Total parts}}\times 100\] and to find the weight, we can use \[\text{Weight of carbon}=percent\times \text{weight of chalk}\]. We should have the required data to substitute in it.