# NCERT Class 8 Mathematics Solutions: Chapter 13 – Direct and Inverse Proportions Exercise 13.2 Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. A factory requires machines to produce a given number of articles in days. How many machines would be required to produce the same number of articles in days?

Answer:

Consider, the number of machines required be

Days | ||

Machines |

The number of machines and the number of days are in inverse proportion.

So, machines would be required.

2. A car takes hours to reach a destination by travelling at the speed of . How long will it take when the car travels at the speed of ?

Answer:

Consider, The number of hours be .

Speed (in km/hr) | ||

Time (in hours) |

So, the speed of car and time are in inverse proportion.

hrs.

So, the car will take hours to reach its destination.

3. Two persons could fit new windows in a house in days.

(i) One of the persons fell ill before the work started. How long would the job take now?

(ii) How many persons would be needed to fit the windows in one day?

Answer:

(i) Consider, the number of days be .

Persons | ||

Days |

Inverse proportion:

days

(ii) Consider,

The number of persons be .

Person | ||

Days |

Inverse proportion:

Persons

4. A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?

Answer:

Consider, the duration of each period be x.

Period 8 9

Duration of period (in minutes) 45 x

The number of periods and the duration of periods are in inverse proportion.

⇾ 8/9 = x/45

⇾ x × 9 = 8 × 45

⇾ x = (8 × 45) /9

⇾ x = 40 Minutes

So, the duration of each period would be 40 minutes.