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**Question 1:** A mixture of paint is prepared by mixing 1 part of green pigments with 6 parts of the base. In the following table, find the parts of base needed to be added.

Parts of green pigment | 1 | 4 | 5 | 6 |

Parts of base | 6 | x_{1} | x_{2} | x_{3} |

**Solution: **Here, as the base increased, the required number of green pigments will also increase.

âˆ´ The quantity vary directly:

Thus, the required unknown quantities are: x_{1} = 24, x_{2} = 30, and x_{3} = 36.**Question 2:** A machine fills 540 bottles in six hours. How many bottles will it fill in five hours?**Solution:**

Numbers of bottles filled | Number of hours |

540 | 6 |

x | 5 |

Let the required number of bottles to be filled in 5 hours = x

Since, more number of bottles, more number of hours would be required.

âˆ´ The given quantities very directly.

= 5 * 90 = 450

Thus, the required number of bottles = 450.**Question 3: **Jagmeet has a road map with a scale of 1 cm = 20 km. He drives on a road for 72 km. What would be his distance covered in the map?**Solution: **Let the distance covered on the map be â€˜xâ€™ km.

âˆ´ We have:

Actual distance covered on the road (in km) | Distance covered (represented) on the map ( in cm) |

20 | 1 |

72 | x |

It is a case of direct variation.

Thus, the required distance on the map is represented as 3.4 cm.**Question 4:** In a PG House, the food provision for 20 persons is for 10 days. How long would the food provision last if there were 5 more persons in that PG house?.**Solution: **Number of persons added = 5

âˆ´ Present number of persons = 20 + 5 = 25

Since, for more persons, the food will last less number of days.

âˆ´ It is a case of inverse variation.

âˆ´25 * x = 20 * 10

âˆ´ The food will now last for 8 days.**Question 5:** A contractor estimates that 5 persons complete a task in 4 days. If he uses 4 persons instead of 5, how long should they take to complete the task?**Solution: **More is the number of persons, less is the time to complete the task.

âˆ´ It is a case of inverse variation,

Now, we have:

Number of presons | Number of days to complete the task |

5 | 4 |

4 | x |

5 * 4 = 4 * x

Thus, the required number of days = 5.**Question 6:** A school has 9 periods a day each of 50 minutes duration. How many period will there be, if the duration of every period is reduced by 5 minutes?**Solution: **Presents duration each period = (50 â€“ 5) minutes = 45 minutes.

Let the present number of period be â€˜xâ€™.

Since, more the number of periods, less is the duration of a period.

âˆ´ It is a case of inverse variation.

We have:

âˆ´ 9 * 50 = x * 45

Thus, the required number of periods = 10.

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