# Ex.13.1 Q4 Direct and Inverse Proportions Solution - NCERT Maths Class 8

## Question

A machine in a soft drink factory fills \(840\) bottles in \(6\) hours. How many bottles it will fill in five hours?

## Text Solution

**What is Known?**

\(840\) bottles can be filled in \(6\) hours.

**What is Unknown?**

Bottles filled in \(5 \) hours.

**Reasoning:**

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

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

Where* \(k\)* is a constant.

**Steps:**

No of bottles | Time in hours |

\({x}_{1}=840\) | \({y}_{1}=6\) |

\({x}_{2}=?\) | \({y}_{2}=5\) |

So, the number of bottles filled, and numbers of hours are directly proportional to each other.

\[\begin{align} & \frac{{{x}_{1}}}{{{y}_{1}}}=\frac{{{x}_{2}}}{{{y}_{2}}} \\ & \frac{840}{6}=\frac{{{x}_{2}}}{5} \\ & 6{{x}_{2}}=840\,\times \,5 \\ & {{x}_{2}}=\frac{840\times 5}{6} \\ & {{x}_{2}}=700 \end{align}\]

\(700 \) bottles will be filled in \(5 \) hours.