8th Class Mathematics Direct and Inverse Proportions

  • question_answer 10)                 A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?

    Answer:

                    Two quantities \[x\] and \[y\] which vary in direct proportion have the relation \[x=ky\]               or  \[\frac{x}{y}=k\]                        Here, \[k=\frac{\text{number}\,\text{of}\,\text{km}\,\,\text{it}\,\text{can}\,\text{travel}}{\text{time}\,\text{in}\,\text{hours}}\] \[=\frac{14}{\left( \frac{25}{60} \right)}=\frac{14\times 60}{25}\] \[=\frac{168}{5}\] Now, \[x\] is the distance travelled in 5 hours Using the relation \[x=ky,\] we obtain \[x=\frac{168}{5}\times 5\] \[\Rightarrow \]               \[x=168\] Hence, it can travel 168 km.

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