Ex.8.3 Q7 Compairing Quantities - NCERT Maths Class 7

Go back to  'Ex.8.3'

Question

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

(ii) If in a stick of chalk, carbon is \(3\rm g,\) what is the weight of the chalk stick?

 Video Solution
Comparing Quantities
Ex 8.3 | Question 7

Text Solution

What is Known?

(i) Ratio in which chalk contains calcium, carbon and oxygen \((10:3:12). \)

(ii) Weight of carbon in stick of chalk \((3\rm g).\)

What is Unknown?

(i) The percentage of carbon in chalk.

(ii) what is the weight of the chalk stick if it contains \(3\rm g\) carbon.

Reasoning:

(i) To find the percentage of carbon, use the following formula

Percentage of carbon 

\[\begin{align}=\frac{\text{Parts of carbon}}{\text{Sum of all parts}} \times 100\end{align} \]

(ii) the concept of percentage can be used find the total quantity.

Steps:

Parts of carbon \(= 3\) and sum of all parts \(= 10 + 3 + 12 = 25\)

Percentage of carbon 

\[\begin{align}&= \frac{{{\rm{Parts}}\;{\rm{of}}\;{\rm{carbon}}}}{{{\rm{Sum}}\;{\rm{of}}\;{\rm{all}}\;{\rm{parts}}}} \times {\rm{100}}\\&=\frac{{\rm{3}}}{{{\rm{25}}}} \times {\rm{100}}\\&= 12\% \end{align}\]

(ii) Carbon in the stick of chalk \(= 3\rm g,\) and carbon percentage in chalk is \(12\%.\)

This means \(12\%\) of carbon \(= 3\rm g\) 

Let total quantity be \(Q\)

\[{\rm{I}}{\rm{.E}}{\rm{.}}\frac{{{\rm{12}}}}{{{\rm{100}}\;}} \times {\rm{Q}}\,{\rm{ = }}\,{\rm{3}}\]\[{\rm{Total}}\,{\rm{Quantity}}\,{\rm{ = }}\,{\rm{3}} \times \frac{{{\rm{100}}}}{{{\rm{12}}}}\;\,{\rm{ = }}\,{\rm{25}}\,{\rm{g}}\]