# Ex.13.1 Q10 Direct and Inverse Proportions Solution - NCERT Maths Class 8

## Question

A loaded truck travels \(14\,\rm{km}\) in \(25\) minutes. If the speed remains the same, how far it travels in \(5\) hours?

## Text Solution

**What is Known?**

Truck travels \(14\,\rm{km}\) in \(25 \) minutes.

**What is Unknown?**

Distance travelled in \(5\) hours.

**Reasoning:**

Two numbers \(x\) and \(y\) are said in direct proportion if,

\[\begin{align}\frac{x}{y} = k,\quad x = k\,y\end{align}\]

Where \(k\) is a constant.

**Steps:**

In \(25\) minutes, it travels \(14 \,\rm{km}\). In \(5\) hours, it will travel more distance. So, it is a case of direct proportion.

Distance |
Time in minutes |

\({{\rm{14}}}\) | \({{\rm{25}}}\) |

\({\,{\rm{?}}}\) |
\(5 \times 60 \) (\(1\) hour \(=\) \(60\) minutes) |

[For comparison the unit should be same]

\[\begin{align}\frac{{{x_1}}}{{{y_1}}} &= \frac{{{x_2}}}{{{y_2}}}\\\frac{{14}}{{25}} &= \frac{{{x_2}}}{{5 \times 60}}\\25\,{x_2} &= 5 \times 60 \times 14\\{x_2} &= \frac{{5 \times 60 \times 14}}{{25}}\\{x_2} &= 168\;{\rm{km}}\end{align}\]

Hence the truck can travel \(168 \,\rm{km}\) in \(5\) hours.