Question 1.

Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take?

Solution:

Let 6 workers take x days and 15 workers take y days to weed the field.

The number of workers and the time required to weed the field are in inverse proportion.

∴ 6 × x = 5 × 12

= 4 days

∴ 6 workers will take 10 days and 15 workers will take 4 days to weed the field.

Question 2.

Mohanrao took 10 days to finish a book, reading 40 pages every day. How many pages must he read in a day to finish it in 8 days?

Solution:

Let Mohanrao read x pages every day to finish the book in 8 days.

The number of pages read per day and the days required to finish the book are in inverse proportion.

∴ 8 × x = 10 × 40

= 50

∴ Mohanrao will have to read 50 pages every day to finish the book in 8 days.

Question 3.

Mary cycles at 6 km per hour. How long will she take to reach her Aunt’s house which is 12 km away? If she cycles at a speed of 4 km/hr, how long would she take?

Solution:

Speed of the cycle = 6 km / hr

Distance travelled to reach her Aunt’s house = 12 km

= 2 hours

Let the time required when the speed of the cycle is 4 km/hr be x hours.

The speed of the cycle and the time required to travel the same distance are in inverse proportion.

∴ 4 × x = 6 × 2

∴ Mary will require 2 hours if she is cycling at 6 km/hr and 3 hours if she is cycling at 4 km/hr to reach her Aunt’s house.

Question 4.

The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people?

Solution:

Let the stock of grain last for x days for 6000 people.

The number of people and the days for which stock will last are in inverse proportion.

∴ 6000 × x = 4000 × 30

∴ The stock of grain will last for 20 days for 6000 people.

**Intext Questions and Activities**

Question 1.

Students of a certain school went for a picnic to a farm by bus. Here are some of their experiences. Say whether the quantities in each are in direct or in inverse proportion.

(Textbook pg. no. 65 and 66)

i. Each student paid Rs 60 for the expenses.

As there were 45 students,___rupees were collected.

Had there been 50 students,___rupees would have been collected.

The number of students and money collected are in___proportion.

ii. The sweets shop near the school gave 90 laddoos for the picnic.

If 45 students go for the picnic, each will get___laddoos.

If 30 students go for the picnic, each will get___laddoos.

The number of students and that of laddoos each one gets are in___proportion.

iii. The farm is 120 km away from the school.

The bus went to the farm at a speed of 40 km per hour and took___hours.

On the return trip, the speed was 60 km per hour. Therefore, it took___hours.

The speed of the bus and the time it takes are in___proportion.

iv. The farmer picked 180 bors from his trees.

He gave them equally to 45 students. Each student got___bors.

Had there been 60 students, each would have got___bors.

The number of students and the number of bors each one gets are in___proportion.

Solution:

i. Rs 2700, Rs 3000, direct

ii. 2,3, inverse

iii. 3,2, inverse

iv. 4,3, inverse