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# Exercise 4.1 (Direct Proportion)

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 = ₹ 84.

(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

x1 / y1 = x2 / y2

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,

x1 / y1 = x2 / y2

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,

x1 / y1 = x2 / y2

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              8m             x m

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

So, it is in direct proportion

Hence,

x1 / y1 = x2 / y2

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, x1 / y1 = x2 / y2

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, x1 / y1 = x2 / y2

(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

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

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

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

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

Exercise 4.1

1. (i) ₹ 84 (ii) 21kg. (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

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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