Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 4 Direct and Inverse Proportion Ex 4.1

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Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 4 Direct and Inverse Proportion Ex 4.1

Fill in the blanks.

(i) If the cost of 8 apples is 56 then the cost of 12 apples is ____.
(ii) If the weight of one fruit box is \(3 \frac{1}{2}\) kg, then the weight of 6 such boxes is ____.
(iii) A car travels 60 km with 3 liters of petrol. If the car has to cover the distance of
200 km, it requires ___ liters of the petrol.
(iv) If 7 m cloth costs ₹ 294, then the cost of 5m of cloth is ____.
(v) If a machine in a cool drinks factory fills 600 bottles in 5 hrs, then it will fill _____ bottles in 3 hours.
Solutions:
(i) 84
(ii) 21 kg
(iii) 10
(iv) ₹ 210
(v) 360

Question 2.
Say True or False
(i) Distance travelled by a bus and time taken are in direct proportion.
(ii) Expenditure of a family to number of members of the family are in direct proportion.
(iii) Number of students in a hostel and consumption of food are not in direct proportion.
(iv) If Mallika walks 1km in 20 minutes, then she can convert 3km in 1 hour.
(v) If 12 men can dig a pond in 8 days, then 18 men can dig it in 6 days.
Solutions:
(i) True
(ii) True
(iii) False
(iv) True
(v) False

Question 3.
A dozen bananas costs ₹ 20. What is the price of 48 bananas ?
Solution:
Let the required price be ₹ x. As the number of bananas increases price also increases
∴ Number of bananas and cost are in direct proportion.

Question 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 ₹ 1680?
Solution:
Let the required number of students be x.

As the number of students increases the entry fees also increases.
∴ They are in direct proportion .

∴ The number of students entered magic show = 42

Question 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?
Solution:
Let the number of people attended the party be x.

As the number of trips increases, number of people also increases.
∴ They are in direct proportion.


180 people attend the party in 12 trips

Question 6.
The shadow of a pole with height of 8m is 6m. If the shadow of another pole measured at the same time is 30m, find the height of the pole?
Solution:
Let the required height of the pole be ‘x’ m.

Height of the pole and its shadow are in direct proportion

∴ Height of the pole x = 40m.

Question 7.
A postman can sort out 738 letters in 6 hours. How many letters can be sorted in 9 hours?
Solution:
Let the required number of letters be x.

They are in direct proportion.

In 9 hours 1107 letters can be sorted.

Question 8.
If half a meter of cloth costs ₹ 15. Find the cost of \(8 \frac{1}{3}\) meters of the same cloth.
Solution:
Let the cost of cloth required be x.

Cost and length are in direct proportion.

Question 9.
The weight of 72 books is 9 kg. What is the weight of 40 such books (using unitary method)
Solution:
Weight of 72 books = 9 kg = 9000 g
∴ Weight of 1 book = \(\frac{9000}{72}\) = 125 g
∴ Weight of 40 books = 125 × 40 g = 5000 g = 5 kg.
Weight of 40 books = 5 kg

Question 10.
Thamarai pages ₹ 7500 as rent for 3 months. With the same rate how much does she have to pay for 1 year (using unitary method).
Solution:
Rent paid by Thamarai for 3 months = ₹ 7500
∴ Rent paid for 1 month = \(\frac{7500}{3}\) = 2500
Rent paid for 1 year or 12 moths = 2500 × 12 = ₹ 30,000
For 1 year rent to be paid = ₹ 30,000

Question 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).
Solution:

∴ 20 men can reap the field in 10 days.

Question 12.
Valli purchase 10 pens for ₹ 180 and Kamala boys 8 pens for ₹ 96. Can you say who bought the pen cheaper (using unitary method).
Solution:

∴ Kamala bought the pen cheaper.

Question 13.
A motorbike requires 2 liters of petrol to cover 100 kilometres. How many liters of petrol will be required to cover 250 kilometers? (using unitary method).
Solution:
To cover 100 km quantity of petrol required = 2 litres

5 litres of petrol required to cover 250 km

Objective Type Questions

Question 14.
If the cost of 3 books is ₹ 90, then find the cost of 12 books.
(i) ₹ 300
(ii) ₹ 320
(iii) ₹ 360
(iv) ₹ 400

Solution:
(iii) ₹ 360

Question 15.
If Mani buys 5 kg of potatoes for ₹ 75 then he can buy ₹ 105.
(i) 6
(ii) 7
(iii) 8
(iv) 5

Solution:
(ii) 7

Question 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

Solution:
(iv) 147

Question 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
Solution:
(ii) 10

Question 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

Solution:
(i) 9