7 th maths chapter 4 ||| 4.1

7th Standard Mathematics — Chapter 4: Direct and Inverse Proportion

Exercise 4.1 Solutions

1. Fill in the blanks

1. If the cost of 8 apples is ₹ 56, then the cost of 12 apples is ₹ 84.
   Working: Cost per apple = 56 ÷ 8 = ₹ 7. Cost of 12 apples = 12 × 7 = ₹ 84.
2. If the weight of one fruit box is 3 ½ kg, then the weight of 6 such boxes is 21 kg.
   Working: 3 ½ = 7/2. Weight of 6 boxes = (7/2) × 6 = 21 kg.
3. 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.
   Working: Petrol needed per km = 3/60 = 1/20 liter. For 200 km = 200 ÷ 20 = 10 liters.
4. If the cost of 7 m cloth is ₹ 294, then the cost of 5 m of cloth is ₹ 210.
   Working: Cost per meter = 294 ÷ 7 = ₹ 42. Cost for 5 m = 5 × 42 = ₹ 210.
5. If a machine in a cool drinks factory fills 600 bottles in 5 hrs, then it will fill 360 bottles in 3 hours.
   Working: Bottles per hour = 600 ÷ 5 = 120. In 3 hours = 120 × 3 = 360 bottles.

2. Say True or False

1. Distance travelled by a bus and time taken are in direct proportion.
   Answer: True
   Reason: At a constant speed, more distance requires more time.
2. Expenditure of a family to number of members of the family are in direct proportion.
   Answer: True
   Reason: More members in a family generally lead to higher overall expenditure.
3. Number of students in a hostel and consumption of food are not in direct proportion.
   Answer: False
   Reason: They are in direct proportion because more students consume more food.
4. If Mallika walks 1 km in 20 minutes, then she can cover 3 km in 1 hour.
   Answer: True
   Reason: 1 hour = 60 minutes. Time for 3 km = 3 × 20 = 60 minutes = 1 hour.
5. If 12 men can dig a pond in 8 days, then 18 men can dig it in 6 days.
   Answer: False
   Reason: In inverse proportion, 12 × 8 = 96 man-days. For 18 men, days required = 96 ÷ 18 = 5 ⅓ days (not 6 days).

3. Price of Bananas Problem

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

Solution:

• 1 dozen = 12 bananas
• Cost of 12 bananas = ₹ 20
• Number of dozens in 48 bananas = 48 ÷ 12 = 4 dozens

Price of 48 bananas = 4 × ₹ 20 = ₹ 80

Answer: The price of 48 bananas is ₹ 80.

4. Magic Show Entry Fee Problem

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?

Solution:

• Fee per student = ₹ 840 ÷ 21 = ₹ 40
• Total amount paid = ₹ 1,680

Number of students = 1,680 ÷ 40 = 42 students

Answer: 42 students entered the magic show.

5. Hotel Lift Trips Problem

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?

Solution:

• People carried per trip = 120 ÷ 8 = 15 people
• Number of trips = 12

Total people = 12 × 15 = 180 people

Answer: 180 people would have attended the party.

6. Shadow of a Pole Problem

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?

Solution:

Height and shadow length are in direct proportion:

Height / Shadow = 8 / 6 = Height / 30

Height = (8 × 30) ÷ 6 = 8 × 5 = 40 m

Answer: The height of the pole is 40 m.

7. Letter Sorting Problem

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

Solution:

• Letters sorted per hour = 738 ÷ 6 = 123 letters

Letters sorted in 9 hours = 123 × 9 = 1,107 letters

Answer: 1,107 letters can be sorted in 9 hours.

8. Cloth Cost Problem

If half a meter of cloth costs ₹ 15. Find the cost of 8 ⅓ meters of the same cloth.

Solution:

• Cost of ½ m cloth = ₹ 15 ⇒ Cost of 1 m cloth = ₹ 15 × 2 = ₹ 30
• Length of cloth = 8 ⅓ m = 25/3 m

Total Cost = (25/3) × 30 = 25 × 10 = ₹ 250

Answer: The cost of 8 ⅓ meters of cloth is ₹ 250.

9. Weight of Books (Unitary Method)

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

Solution:

• Weight of 72 books = 9 kg
• Weight of 1 book = 9 ÷ 72 = 1/8 kg

Weight of 40 books = 40 × (1/8) = 5 kg

Answer: The weight of 40 books is 5 kg.

10. Rent Calculation (Unitary Method)

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)

Solution:

• 1 year = 12 months
• Rent for 3 months = ₹ 7,500
• Rent for 1 month = 7,500 ÷ 3 = ₹ 2,500

Rent for 12 months = 2,500 × 12 = ₹ 30,000

Answer: She has to pay ₹ 30,000 for 1 year.

11. Comparing Pen Cost (Unitary Method)

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

Solution:

• Cost of 1 pen for Valli = ₹ 180 ÷ 10 = ₹ 18
• Cost of 1 pen for Kamala = ₹ 96 ÷ 8 = ₹ 12

Since ₹ 12 < ₹ 18, Kamala bought the pens cheaper.

Answer: Kamala bought the pens cheaper.

12. Motorbike Fuel Calculation (Unitary Method)

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)

Solution:

• Petrol required for 100 km = 2 litres
• Petrol required for 1 km = 2 ÷ 100 = 1/50 litre

Petrol required for 250 km = 250 × (1/50) = 5 litres

Answer: 5 litres of petrol will be required.