question_answer

(a) Chalk contains calcium carbon and oxygen in the ratio 10: 3:12. Find the percentage of carbon in chalk.

(b) If in a stick of chalk carbon is 3 g what is the weight of the chalk stick?

Answer:

(a) Given, ratio of calcium, carbon and oxygen in a chalk stick are 10: 3: 12.

Sum of the parts = 10 + 3 + 12 = 25

∴ Percentage of carbon in chalk stick

\[=\left( \frac{Part\text{ }of\text{ }carbon\text{ }in\text{ }chalk\text{ }stick}{Total\text{ }part\text{ }of\text{ }chalk}\times 100 \right)%\]

\[=\left( \frac{3}{25}\times 100 \right)%=(3\times 4)%=12%\]

Hence, the percentage of carbon in a chalk stick is 12%.

(b) Let the weight of the chalk stick be x g.

Now, weight of carbon = 3 g (which is 12% of chalk)

∴  12% of x = 3

\[\frac{12}{100}\times x=3\]

\[x=\frac{3\times 100}{12}=25g\]

Hence, the weight of the chalk stick is 25 g.