Selina Solutions Concise Mathematics Class 6 Chapter 11 Ratio
Exercise 10(A)
1.Express each of the following ratios in its simplest form:
(a)
(i) 4:6
Answer : 4:6=2:3
Answer: 48:54 = 8:9
(iii) 200:250
Answer : 4:5
(b) (i) 5 kg: 800 g
Answer: 5 kg = 5000 g
5000 g : 800 g = 25:4
Answer: 2 m = 200 cm
Ratio =30 cm: 200 cm = 3:20
(iii) 3 m: 90 cm
Answer: 3 m = 300 cm
300 cm : 90 cm = 10:3
iv) 2 years: 9 months
Answer : 2 years = 24 month
v) 24 month : 9 month = 8:3
vi) 1 hour: 45 min
Answer: 1 hour= 60 min 60 min: 45 min= 4:3
(iii) 4 min: 45 sec
Answer: 4 min = 240 sec 240 sec: 45 sec = 16:3
(c) (i) 1 1/2 : 2 1/2= 3/2 : 5/2
=2 x 3/2 : 2 x 5/2 = 3:5
ii) 3 1/2 : 7 = 7/2 : 7= 2 x 7/2 : 2 x 7= 7 : 14 = 1:2
iii) 2 1/3. : 3 1/2 : 1 1/4 = 7/3 : 5/2 : 5/4 ( LCM= 12)
Ratio = 7/3 x 12 : 7/2 x 12 : 5/4 x 12= 28: 42: 15
(iv) x²:4x
x²:4x = x:4
(v) 2.5:1.5 =
= 5:3
(vi) 2.5 : 5 =
2. A field is 80 m long and 60 m wide. Find the ratio of its
width to its length.
Answer: 60:80 = 3:4
3. State, true or false:
(i) A ratio equivalent to 7:9 is
27:21
Answer: False (Correct ratio is ( 21:27 )
(ii) A ratio
equivalent to 5:4 is 240:192
Answer: True
(iii) A ratio of
250 g and 3 kg is 1:12
Answer: False (Correct ratio is 1:12)
4. Is the ratio of 15 kg and 35 kg the same as the ratio of
6 years and 14 years?
Answer: Yes (Both simplify to 3:7 )
5. Is the ratio of 6 g and 15 g the same as the ratio of 36
cm and 90 cm?
Answer: Yes (Both simplify to 2:5 )
Answer: 3.5 m = 350 cm 2.8 m = 280 cm
350:475:280 = 70:95:56
7. Find the ratio between 5 dozen and 2 scores.
Answer: 5
dozen= 60
2 scores= 40
Ratio= 60:40 = 3:2
Exercise 10(B)
1. The monthly salary of a person is ₹ 12,000 and his
monthly expenditure is ₹ 8,500. Find the ratio of his:
(i) Salary to
expenditure
Answer: 12000:8500 = 24:17
(ii) Expenditure to
savings
Answer: Savings = 12000 - 8500 = 3500
Ratio 8500:3500 = 17:7
(iii) Savings to
salary
Answer: 3500:12000 = 7:24
2. The strength of a class is 65, including 30 girls. Find
the ratio of the number of:
(i) Girls to boys
Answer: Boys = 65 -
30 = 35
ratio 30:35 = 6:7
(ii) Boys to the
whole class
Answer: 35:65 = 7:13
(iii) The whole
class to girls
Answer: 65:30 = 13:6
3. The weekly expenses of a boy have increased from ₹ 1,500
to ₹2,250. Find the ratio of:
(i) Increase in
expenses to original expenses
Answer: Increase in
expenses = 2250 - 1500 = 750
Ratio =750:1500 = 1:2
(ii) Original
expenses to increased expenses
Answer: 1500:2250 =
2:3
(iii) Increased
expenses to increase in expenses
Answer: 2250:750 = 3:1
4. Reduce each of the following ratios to their lowest
terms:
(i) 1 hour 20 min :
2 hours
Answer: 80min :120min = 2:3
(ii) 4 weeks:
49 days
Answer: 28:49 = 4:7
(iii) 3 years 4 months : 5 years 5 months
Answer: 40:65 =
8:13
(iv) 2 m 40 cm: 1 m
44 cm
Answer: 240:144 =
5:3
(v) 5 kg 500 g : 2 kg 750 g
Answer: 5500:2750 = 2:1
5. Two numbers are in the ratio 9:2. If the smaller number
is 320, find the larger number.
Answer: larger no /
smaller no. 9/2
Larger no .= 9/2 x 320
= 1440
6. A bus travels 180 km in 3 hours and a train travels 450
km in 5 hours. Find the ratio of the speed of the train to the speed of the
bus.
Answer: Bus speed =
180/3= 60 km/h
Train speed =450/5= 90 km/h Ratio = 90:60 = 3:2
7. In winters, a school opens at 10 a.m. and closes at 3.30
p.m. If the lunch interval is of 30 minutes, find the ratio of the lunch
interval to the total time of the class periods.
Answer: Total time
330 min Total class period = 5 hours = 300min
Break interval = 30 min
Ratio = 30:300 = 1:10
8. Rohit goes to his school by car at 60 km per hour and
Manoj goes to the same school by scooty at 40 km per hour. If they both live in
the same locality, find the ratio between the time taken by Rohit and Manoj to
reach their school.
Answer: Let
distance covered be D.
Time taken = D/ speed
Time taken by car= D/ 60 hour
Time taken by scooty= D/ 40 hour
Ratio= D/60 : D/40.= D/ 60 ÷ D/ 40= D/ 60 x 40/D= 2:3
9. In a club having 360 members, 40 play carrom, 96 play
table tennis, 144 play badminton, and the remaining members play volleyball. If
no member plays two or more games, find the ratio of members who play
(i) Carrom to the
number of those who play badminton.
40:144 = 5:18
(ii) Badminton to
the number of those who play table-tennis.
144:96 = 3:2
(iii) Table tennis
to the number of those who play volleyball.
Volleyball players
= 360 – (40 + 96 + 144) = 80
Ratio = 96:80 = 6:5
(iv) Volleyball to
the number of those who play other games.
80:280 = 2:7
10. The length of a pencil is 18 cm and its radius is 0.4 cm. Find the ratio of its length to its diameter.
Answer: Diameter of the pencil = 2 × radius = 2 × 0.4 cm = 0.8 cm.
Ratio = Length : Diameter = 18 cm : 0.8 cm = 18 : 0.8 = 180 : 8 = 45 : 2.
11. Ratio of the distance of the school from A's home and from B's home is 2:1.
Answer: (1) Who lives nearer to the school?
- B lives nearer to the school because the ratio 2:1 indicates A lives twice as far from the school as B.
(ii) Complete the following table:
Distance (in km) from A's home to school | Distance (in km) from B's home to the same school
4 | 2
18 | 9
8 | 4
16 | 8
6 | 3
12..The student-teacher ratio in a school is 45:2. If there are 4050 students in the school, how many teachers are there in the school?
Answer: Student-Teacher Ratio = 45:2.
Number of teachers = (Number of students / Students per teacher) x Teachers per 45 students = (4050 / 45) x 2 = 90 x 2 = 180 teachers.
Exercise 10(C)
1. ₹ 120 is to be divided between Hari and Gopi in the ratio
5:3. How much does each get?
Answer : Sum of ratio = 8
Hari gets 5/8 x 120 = ₹75,
Gopi gets 3/8 x 120 = ₹45.
2. Divide 72 in the ratio 2 1/2:1 1/2
Answer: 5/2 x2 : 3/2 x2= 5:3
Sum of ratio=8
First part = 5/8 x 72= 45
Second part= 3/8 x72= 27
3.Divide 81 into three parts in the ratio 2:3:4.
Answer: sum of ratio = 9
First part= 2/9 x 81
Second part= 3/9 x 81
Third part = 4/ 9 x 81
18:27:36
4. Divide 10,400 among A, B, and C in the ratio 1/2 : 1/3 : 1/4.
Answer: A:B:C = ½ x 12 : 1/3 x12 : ¼ x12. ( LCM 2 ,3 and 4 = 12)
6:4:3
Sum of ratios = 13
A gets 6/13 x 10400
=₹4800,
B gets 4/13 x10400
=₹3200,
C gets 3/13 x 10400
=₹2400.
5. A profit of 2,500 is to be shared among three persons in the ratio 6:9:10. How much does each person get?
Answer: sum of ratios= 6+9+10= 25
The shares of
A = 6/25 x 2500= ₹600,
B= 9/25 x 2500 = ₹900, and
C= 10/25 x 2500 = ₹1000 respectively.
6. The angles of a triangle are in the ratio 3:7:8. Find the greatest and the smallest angles.
Answer: sum of ratios= 18
Greatest angle is 8/18 x 180 = 80,
smallest angle is 3/18 x 180 = 30.
7. The sides of a triangle are in the ratio 3:2:4. If the perimeter of the triangle is 27 cm, find the length of each side.
Answer: perimeter= 3x + 2x + 4x = 27
x = 27/9 = 3
The sides are 9 cm, 6 cm, and 12 cm.
8. An alloy of zinc and copper weighs 12 1/2 kg. If, in the alloy, the ratio of zinc and copper is 1:4, find the weight of copper in it.
Answer: sum of ratios= 5
Weight of copper= 4/5 x 25/2
Weight of copper is 10 kg.
9. How will 31,500 be shared between A, B, and C, if A gets double of what B gets, and B gets double of what C gets?
Answer:Let C = 1, B= double of C = 2 , A= 2B = 4
Ratio- 4:2:1
Sum of ratios= 7
A gets 4/7 x 31500 = ₹18,000,
B gets. 2/7 x 31500 = ₹9,000,
C gets 1/7 x 31500 =✓ ₹4,500.
10. Mr. Gupta divides 81,000 among his three children, Ashok, Mohit, and Geeta, in such a way that Ashok gets four times what Mohit gets and Mohit gets 2.5 times what Geeta gets. Find the share of each of them.Answer: Let share of Geeta be 1, Mohit will be 2.5 and Ashok as four times Mohit so = 10
ratio of share of Ashok,Mohit and Geeta = 10: 2.5:1or 20. : 5 : 2
Sum = 27
Ashok gets 20/27 x 81000 = ₹60,000,
Mohit gets 5/27 x 81000 = ₹15,000,
Geeta gets 1/27 x 81000 = ₹6000.
11. Which ratio is greater:
(i) 8/15 or 5/9
Answer: 5/9
(ii) 3/7 or 6/13
Answer: 3/7
12. Which ratio is smaller:
(i) 9/17 or 8/15
Answer: 9/17
(ii) 7/15 or 15/32
Answer 7/15
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