Fill in the blanks, Find the value of the following, Objective type questions, Text Book Back Exercises Questions with Answers, Solution

**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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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 *x*_{1} *y*_{1} = *x*_{2} *y*_{2}

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

Tags : Questions with Answers, Solution | Term 1 Chapter 4 | 7th Maths , 7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion : Exercise 4.2 (Inverse Proportion) | Questions with Answers, Solution | Term 1 Chapter 4 | 7th Maths

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