NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

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Ans : A table Of the given information is formed as 
\(\begin{array}{|c|c|c|c|c|}\hline \text { Number of hours } & {4} & {8} & {12} & {24} \\ \hline \text { Parking charges (in Rs) } & {60} & {100} & {140} & {180} \\ \hline\end{array}\) 
The ratio of parking charges to the respective number Of hours (Rs/ hour) can be calculated as 
\(\frac{60}{4}=15, \quad \frac{100}{8}=\frac{25}{2}, \frac{140}{12}=\frac{35}{3}, \frac{180}{24}=\frac{15}{2}\)
As each ratio is not same, therefore, the parking charges are not in a direct proportion to the parking time. 

Ans : The given mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. For more parts of red pigments, the parts of the base will also be more. 
Therefore, the parts of red pigments and the parts Of base are in direct proportion. 
The given information in the form of a table is as follows. 
\(\begin{array}{|c|c|c|c|c|}\hline \text { Parts of red pigment } & {1} & {4} & {7} & {12} & {20} \\ \hline \text { Parts of base } & {8} & {x_{1}} & {x_{2}} & {x_{3}} \\ \hline\end{array}\) 
According to direct proportion , 
\(\begin{array}{l}{\frac{x_{1}}{4}=\frac{8}{1} \Rightarrow x_{1}=4 \times 8=32} \\ {\frac{x_{2}}{7}=\frac{8}{1} \Rightarrow x_{2}=7 \times 8=56} \\ {\frac{x_{3}}{12}=\frac{8}{1} \Rightarrow x_{3}=8 \times 12=96} \\ {\frac{x_{4}}{20}=\frac{8}{1} \Rightarrow x_{4}=8 \times 20=160}\end{array}\) 
The Table can be drawn as follows. 
\(\begin{array}{|c|c|c|c|c|c|}\hline \text { Parts of red pigment } & {1} & {4} & {7} & {12} & {20} \\ \hline \text { Parts of base } & {\text { 8 }} & {32} & {56} & {96} & {160} \\ \hline\end{array}\)