Questions with Answers, Solution | Term 1 Chapter 4 | 7th Maths - Exercise 4.1 (Direct Proportion) | 7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion
Chapter: 7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion
Exercise 4.1 (Direct Proportion)
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.
(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 1 km in 20 minutes, then she can cover 3 km in 1 hour.
(v) If 12 men can dig a pond in 8 days, then 18
men can dig it in 6 days.
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
Shadow 6m 30m
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
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) 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
Related Topics