# NCERT Class 8 Mathematics Solutions: Chapter 13 – Direct and Inverse Proportions Exercise 13.1 Part 1 (For CBSE, ICSE, IAS, NET, NRA 2023)

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1. Following are the car parking charges near a railway station up to:

hours,

hours,

hours,

hours,

Check if the parking charges are in direct proportion to the parking time.

Answer:

Charges per hour:

So, the charges per hour are not same, i.e.. ,

So, the parking charges are not in direct proportion to the parking time.

2. A mixture of paint is prepared by mixing part of red pigments with parts of base. In the following table, find the parts of base that need to be added.

Parts of red pigment | 1 | 4 | 7 | 12 | 20 |

Parts of base | 8 | ________ | ________ | ________ | ________ |

Answer:

The ratio of parts of red pigment and parts of base be

When

When

When

Parts of red pigment | 1 | 4 | 7 | 12 | 20 |

Parts of base | 8 | 32 | 56 | 96 | 160 |

3. In Question above, if part of a red pigment requires of base, how much red pigment should we mix with of base?

Answer:

Consider,

The parts of red pigment mix with base be

Parts of red pigment | ||

Parts of base |

Since it is in direct proportion.

parts

So, with base parts red pigment should be mixed.

4. A machine in a soft drink factory fills bottles in six hours. How many bottles will it fill in five hours?

Answer:

Consider,

The number of bottles filled in five hours be .

Hours | ||

Bottles | x |

Here ratio of hours and bottles are in direct proportion

bottles

So, machine will fill bottles in five hours.