Exercise 4.2 (Inverse Proportion)

Exercise 4.2

1. Fill in the blanks.

(i) 16 taps can fill a petrol tank in 18 minutes. The time taken for 9 taps to fill the same tank will be 32 minutes.

(ii) If 40 workers can do a project work in 8 days, then 80 workers can do it in 4 days.

2. 6 pumps are required to fill a water sump in 1 hr 30 minutes. What will be the time taken to fill the sump if one pump is switched off?

Let x be the required time taken to fill the sump.

Number of Pumps                6                                     5

Time Taken                          1 hr 30 mts (90 mts)        x

When the number of pumps decrease. Time taken will be increased. So it is in inverse proportion

Hence x₁ y₁ = x₂ y₂

6 × 90 = 5 × x

 x = [ 6 × 90 ] / 5 = 108 minutes

x = 108 mts = 1 hr 48 mts

Time taken to fill the sump if one pump is switched off = 1 hr 48 mts.

3. A farmer has enough food for 144 ducks for 28 days. If he sells 32 ducks, how long will the food last?

Let x be the required number of days.

Number of ducks          144       112

Number of days             28              x

When number of ducks decrease food last for days will be increased So, it is in inverse proportion

Hence x₁ y₁ = x₂ y₂

144 × 28 = 112 × x

x = ( 144 × 28) / 112 = 36 days

 The food will last for 36 days.

4. It takes 60 days for 10 machines to dig a hole. Assuming that all machines work at the same speed, how long will it take 30 machines to dig the same hole?

Let x be the required number of days.

Number of Machines    10                  30

Number of days             60                 x

When number of machines increase, number of days will be decreased.

So, it is in inverse proportion. 

Hence x₁ y₁ = x₂ y₂

10 × 60 = 30 × x

 x = [ 10 × 60 ] / 30 = 20 days

30 machines will take 20 days to dig the same hole.

5. Forty students stay in a hostel. They had food stock for 30 days. If the students are doubled then for how many days the stock will last?

Let x be the required number of days

Number of students            40            80

Number of days                  30              x

When number of students increase, the number of days the stock last will be decreased. So, it is in inverse proportion.

Hence x₁ y₁ = x₂ y₂

40 × 30 = 80 × x

 x = [ 40 × 30 ] / 80 = 15 days

 The stock will last for 15 days.

6. Meena had enough money to send 8 parcels each weighing 500 grams through a courier service. What would be the weight of each parcel, if she has to send 40 parcels for the same money?

Let x be the required weight of each parcel.

Number of parcels              8              40

Weight in grams                 500              x

When number of parcels increase the weight will be decreased. So, it is in inverse proportion.

Hence x₁ y₁ = x₂ y₂

8 × 500 = 40 × x

 x = [ 8 × 500 ] / 40 = 100 grams

 The weight of each parcel would be 100 grams.

7. It takes 120 minutes to weed a garden with 6 gardeners If the same work is to be done in 30 minutes, how many more gardeners are needed?

Let x be the required number of gardeners.

Time Taken                   120 mts              30 mts

Number of gardeners         6                        x

When time taken decreases the number of gardeners will be increased So, it is in inverse proportion.

Hence x₁ y₁ = x₂ y₂

120 × 6 = 30 × x

x = [120 × 6] / 30 = 24

x = 24

Number of more gardeners needed = 24 – 6

 = 18

18 more gardeners are needed

8. Neelaveni goes by bi-cycle to her school every day. Her average speed is 12km/hr and she reaches school in 20 minutes. What is the increase in speed, if she reaches the school in 15 minutes?

Let x be the required speed

Speed km/hr                        12                  x

Time taken minutes             20                 15

When Time Taken is decreased the speed will be increased.

So, it is in inverse proportion

Hence x₁ y₁ = x₂ y₂

12 × 20 = x × 15

 x = [12 × 20] / 15 = 16

 x = 16 km / hr

The increase in speed = (16 – 12)km/hr.

                                    = 4 km /hr.

9. A toy company requires 36 machines to produce car toys in 54 days. How many machines would be required to produce the same number of car toys in 81 days?

Let x be the required number of machines.

Number of machines         36              x

Number of days                 54             81

When number of days increase, number of machines will be decreased So, it is in inverse proportion.

Hence x₁ y₁ = x₂ y₂

36 × 54 = x × 81

 x = [36 × 54]  / 81 = 24

x = 24

24 machines w ould be required to produce the same number of car toys in 81 days.

Objective type questions

10. 12 cows can graze a field for 10 days. 20 cows can graze the same field for_____ days.

(i) 15

(ii) 18

(iii) 6

(iv) 8

Answer : (iii) 6

11. 4 typists are employed to complete a work in 12 days. If two more typists are added, they will finish the same work in _______ days.

(i) 7

(ii) 8

(iii) 9

(iv) 10

Answer : (ii) 8

ANSWERS

Exercise 4.2

1. (i) 32

(ii) 80

2. 1 hour 48 minutes

3. 36 days

4. 20 days

5. 15 days

6. 100 gm

7. 18

8. 4 km/hr

9. 24

 Objective Type Questions

10. (iii) 6

11. (ii) 8