7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion : Direct Proportion : Exercise 4.1 : Fill in the blanks, Say true or false, Find the value of the following, Objective type questions, Text Book Back Exercises Questions with Answers, Solution

**Exercise 4.1**

**1.
Fill in the blanks**

(i) If the cost of 8 apples is ₹ 56 then the cost
of 12 apples is **[ 56 / 8 ] × 12**

(ii) If the weight of one fruit box is 3 1/2 kg,
then the weight of 6 such boxes is ** 7/2 × 6 = 21 kg**.

(iii) A car travels 60* km *with 3 liters of petrol. If the car has to cover the distance of
200 km, it requires ** 10** liters of petrol.

3/60 × 200

(iv) If 7*
m *cloth costs ₹ 294, then the cost of 5*
m *of cloth is ** ₹ 210**.

(v) If a machine in a cool drinks factory fills
600 bottles in 5 hrs, then it will fill ** 360** bottles in 3 hours.

600 / 5 × 3

**2.
Say True or False**

(i) Distance travelled by a bus and time taken are
in direct proportion.**(True)**

(ii) Expenditure of a family to number of members
of the family are in direct proportion.**(True)**

(iii) Number of students in a hostel and consumption
of food are not in direct proportion.**(False)**

(iv) If Mallika walks 1* km *in 20 minutes, then she can cover 3* km *in 1 hour.**(True)**

(v) If 12 men can dig a pond in 8 days, then 18
men can dig it in 6 days.**(False)**

**3.
A dozen bananas costs ₹ 20. What is the price of 48 bananas?**

Let *x* be the price of
48 bananas

Number of bananas 12 48

Price ₹ 20 *x*

As the number of bananas increases the price also increases.

In the case of direct proportion we take

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

12 / 20 = 48 / *x*

[ 12 × *x* ] / 20 = 48

*x* = [ 48 × 20 ] / 12 = 80

* x* = ₹ 80

**Hence, the price of
48 bananas = ₹ 80**

** **

**4.
A group of 21 students paid ₹ 840 as the entry fee for a magic show.**

**How
many students entered the magic show if the total amount paid was ₹ 1,680?**

Let *x* be the number of
students paid the amount ₹ 1680

Number of students 21
*x*

Amount paid ₹ 840 1680

As the amount increases the number of students also increases

So, it is in direct proportion

We take,

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

21 / 840 = *x* / 1680

[ 21 × 1680 ] / 840 = *x*

*x = *[ 21 × 1680 ] / 840= 42

*x* = 42

**Number of students
entered the magic show = 42.**

** **

**5.
A birthday party is arranged in third floor of a hotel. 120 people take 8 trips
in a lift to go to the party hall. If 12 trips were made how many people would have
attended the party?**

Let x be the number of people would have attended the party.

Number of people 120 *x*

Number of Trips
8 12

As the number, trips increases the number of people also
increases. So it is in direct proportion.

Hence,

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

120 / 8 = *x* / 12

[ 12 × 120 ] / 8 =* x*

*x* = [ 12 × 120 ] / 8 = 180

*x* = ₹ 180

**Number of people
would have attended the party = 180**

** **

**6.
The shadow of a pole with the height of 8
m is 6m. If the shadow of another pole measured at the same time is 30m, find
the height of the pole?**

Let *x* *m* be the height of the pole

Height 8*m x m*

Shadow 6*m* 30*m*

As the length of the shadow increases the height also increases.

So, it is in direct
proportion

Hence,

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

8 / 6 = *x* / 30

*x *= [ 8 × 30 ] / 6 = 40

* x* = 40

**The height of the
pole = 40 m**

** **

**7.
A postman can sort out 738 letters in 6 hours. How many letters can be sorted in
9 hours?**

Let *x *be the number of
letters sorted in 9 hours.

Number of letters sorted 738 *x*

Time (hrs) 6
9

As the time increases the number of letters sorted also
increases

So, it is in direct proportion

Hence, *x*_{1} /
*y*_{1} = *x*_{2} / *y*_{2}

738 / 6 = *x* / 9

*x *= [ 738 × 9 ] / 6 = 1107

*x* =1107

**1107 letters can be
sorted in 9 hours.**

** **

**8.
If half a meter of cloth costs ₹ 15. Find the cost of 8 1/3 meters of the same cloth.**

Let the cost of 8 1/3 meters of cloth is ₹ *x*.

Length 1/2 *m*
8 1/3 *m*

Cost ₹ 15 *x*

As the length of the cloth increases the cost also increases.

So, it is in direct proportion.

Hence, *x*_{1} /
*y*_{1} = *x*_{2} / *y*_{2}

(½) / 15 = 8 / *x* (1/3 )

[1/2] × [*x* / 15] = 8 [1/3] = 25/3

*x *= 25 / 3 × 2 × 15 = 250

* x *= ₹ 250

The cost of 8 1/3 meters of cloth = ₹ 250

** **

**9.
The weight of 72 books is 9kg. what is the weight of 40 such books? (using unitary
method)**

The weight of 72 books = 9 *kg*

The weight of 1 book = 9/72 *kg*
= 1/8 *kg*

The weight of 40 books = 1/8
× 40 *kg* = 5 *kg*

The weight of 40 books = 5 *kg*

** **

**10.
Thamarai pays ₹ 7500 as rent for 3 months. With the same rate how much does she
have to pay for 1 year? (using unitary method).**

Rent pay for 3 months = ₹ 7500

Rent pay for 1 month = ₹
7500 / 3 = ₹ 2500

Rent pay for 1 year (12 months) = ₹ 2500 × 12

= ₹ 30,000

Rent pay for 1 year = ₹ 30,000

** **

**11.
If 30 men can reap a field in 15 days, then in how many days can 20 men reap the
same field? (using unitary method)**

30 men can reap a field in = 15 days

1 man can reap the field in = 30 × 15 days

= 450 days

20 men can reap the field in = 450 / 20 = 22½ days.

20 men can reap the field in = 22½ days

** **

**12.
Valli purchases 10 pens for ₹ 180 and Kamala buys 8 pens for ₹ 96. Can you say who
bought the pen cheaper? (using unitary method)**

Valli purchases,

Cost of 10 pens = ₹ 180

Cost of 1pen = ₹ 180 / 10 = ₹ 18

Kamala purchases,

Cost of 8 pens = ₹ 96

Cost of 1pen = ₹96 / 8 = ₹ 12

**Kamala bought the
pen cheaper.**

** **

**13.
A motorbike requires 2 litres of petrol to cover 100 kilometers. How many litres
of petrol will be required to cover 250 kilometers? (using unitary method)**

Petrol requires to cover 100 *km*
= 2 litres

Petrol requires to cover
1 *km* = 2 / 100 litres

= 1 / 50 litres

Petrol requires to cover
250 *km* = [1 /50] × 250 litres

**5 litres of petrol
will be required to cover 250 kilometers.**

** **

__Objective
type questions__

**14.
If the cost of 3 books is ₹ 90, then find the cost of 12 books.**

(i) ₹ 300

(ii) ₹ 320

(iii) ₹ 360

(iv) ₹ 400

*Answer :***(iii) ₹ 360**

**15.
If Mani buys 5kg of potatoes for ₹ 75 then he can buy ______kg of potatoes for ₹
105.**

(i) 6

(ii) 7

(iii) 8

(iv) 5

*Answer :***(ii) 7**

**16.
35 cycles were produced in 5 days by a company then______ cycles will be produced
in 21 days.**

(i) 150

(ii) 70

(iii) 100

(iv) 147

*Answer :***(iv) 147**

**17.
An aircraft can accommodate 280 people in 2 trips. It can take ______trips to take
1400 people.**

(i) 8

(ii) 10

(iii) 9

(iv) 12

*Answer :*** (ii)10**

**18.
Suppose 3 kg. of sugar is used to prepare sweets for 50 members, then ____ kg. of
sugar is required for 150 members.**

(i) 9

(ii) 10

(iii) 15

(iv) 6

*Answer :***(i) 9**

**ANSWERS**

**Exercise 4.1 **

1. (i) ₹ 84 (ii) 21*kg*. (iii) 10 litres (iv) ₹ 210 (v) 360

2. (i) True (ii) True (iii) False
(iv) True (v) False

3. ₹ 80

4. 42

5. 180

6. 40* m *

7. 1107

8. ₹ 250

9. 5 *kg*.

10. ₹ 30,000

11. 10 days

12. Kamala

13. 5 litres

** ****Objective Type Questions **

14. (iii) ₹ 360

15. (ii) 7

16. (iv) 147

17. (ii) 10

18. (i) 9

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

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7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion : Exercise 4.1 (Direct Proportion) | Questions with Answers, Solution | Term 1 Chapter 4 | 7th Maths

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