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Chapters
2: Factors and Multiples
3: Whole Numbers
4: Integers
Chapter 5: Fractions
6: Simplification
7: Decimals
8: Algebraic Expressions
9: Linear Equation in One Variable
▶ 10: Ratio, Proportion and Unitary Method
Chapter 11: Line Segment, Ray and Line
Chapter 12: Parallel Lines
Chapter 13: Angles and Their Measurement
Chapter 14: Constructions (Using Ruler and a Pair of Compasses)
Chapter 15: Polygons
Chapter 16: Triangles
Chapter 17: Quadrilaterals
Chapter 18: Circles
Chapter 19: Three-Dimensional Shapes
Chapter 20: Two-Dimensional Reflection Symmetry (Linear Symmetry)
Chapter 21: Concept of Perimeter and Area
Chapter 22: Data Handling
Chapter 23: Pictograph
Chapter 24: Bar Graph
![R.S. Aggarwal solutions for Mathematics [English] Class 6 chapter 10 - Ratio, Proportion and Unitary Method - Shaalaa.com](/images/mathematics-english-class-6_6:33c16d70f7d44841a2f75f8a6c346822.jpg "R.S. Aggarwal solutions for Mathematics [English] Class 6 chapter 10 - Ratio, Proportion and Unitary Method")
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Solutions for Chapter 10: Ratio, Proportion and Unitary Method
Below listed, you can find solutions for Chapter 10 of CBSE R.S. Aggarwal for Mathematics [English] Class 6.
R.S. Aggarwal solutions for Mathematics [English] Class 6 10 Ratio, Proportion and Unitary Method Exercise 10A [Pages 152 - 153]
Find the following ratio in the simplest form:
24 to 56
Find the following ratio in the simplest form:
84 paise to Rs 3
Find the following ratio in the simplest form:
4 kg to 750 g
Find the following ratio in the simplest form:
1.8 kg to 6 kg
Find the following ratio in the simplest form:
48 minutes to 1 hour
Find the following ratio in the simplest form:
2.4 km to 900 m
Express the following ratio in the simplest form:
36 : 90
Express the following ratio in the simplest form:
324 : 144
Express the following ratio in the simplest form:
85 : 561
Express the following ratio in the simplest form:
480 : 384
Express the following ratio in the simplest form:
186 : 403
Express the following ratio in the simplest form:
777 : 1147
Write the following ratio in the simplest form:
Rs 6.30 : Rs 16.80
Write the following ratio in the simplest form:
3 weeks : 30 days
Write the following ratio in the simplest form:
3 m 5 cm : 35 cm
Write the following ratio in the simplest form:
48 min : 2 hours 40 min
Write the following ratio in the simplest form:
1 L 35 mL : 270 mL
Write the following ratio in the simplest form:
4 kg : 2 kg 500 g
Mr. Sahai and his wife are both school teachers and earn Rs 16800 and Rs 10500 per month respectively. Find the ratio of
(i) Mr. Sahai's income to his wife's income;
(ii) Mrs. Sahai's income to her husband's income;
(iii) Mr. Sahai's income to the total income of the two.
Rohit earns Rs 15300 and saves Rs 1224 per month. Find the ratio of
(i) his income and savings:
(ii) his income and expenditure;
(iii) his expenditure and savings.
The ratio of the number of male and female workers in a textile mill is 5 : 3. If there are 115 male workers, what is the number of female workers in the mill?
The boys and the girls in a school are in the ratio 9 : 5. If the total strength of the school is 448, find the number of girls.
Divide Rs 1575 between Kamal and Madhu in the ratio 7 : 2.
Divide Rs 3450 among A, B, and C in the ratio 3 : 5 : 7.
Two numbers are in the ratio 11 : 12 and their sum is 460. Find the numbers.
A 35-cm line segment is divided into two parts in the ratio 4 : 3. Find the length of each part.
A factory produces electric bulbs. If 1 out of every 10 bulbs is defective and the factory produces 630 bulbs per day, find the number of defective bulbs produced each day.
Find the ratio of the price of a pencil to that of a ball pen if pencils cost Rs 96 per score and ball pens cost Rs 50.40 per dozen.
The ratio of the length of a field to its width is 5 : 3. Find its length if the width is 42 metres.
The ratio of income to savings of a family is 11 : 2. Find the expenditure if the savings is Rs 1520.
The ratio of income to the expenditure of a family is 7 : 6. Find the savings if the income is Rs 14000.
The ratio of zinc and copper in an alloy is 7 : 9. If the weight of copper in the alloy is 11.7 kg find the weight of zinc in it.
A bus covers 128 km in 2 hours and a train covers 240 km in 3 hours. Find the ratio of their speeds.
From the given pairs, find which ratio is larger:
(3 : 4) or (9 : 16)
From the given pairs, find which ratio is larger:
(5 : 12) or (17 : 30)
From the given pairs, find which ratio is larger:
(3 : 7) or (4 : 9)
From the given pairs, find which ratio is larger:
(1:2) or (13:27)
Fill in the place holder:
Fill in the place holder:
Fill in the place holder:
R.S. Aggarwal solutions for Mathematics [English] Class 6 10 Ratio, Proportion and Unitary Method Exercise 10B [Page 155]
Determine if the following numbers are in proportion:
4, 6, 8, 12
Determine if the following numbers are in proportion:
7, 42, 13, 78
Determine if the following numbers are in proportion:
33, 121, 9, 96
Determine if the following numbers are in proportion:
22, 33, 42, 63
Determine if the following numbers are in proportion:
32, 48, 70, 210
Determine if the following numbers are in proportion:
150, 200, 250, 300
Verify the following:
60 : 105 : : 84 : 147
Verify the following:
91 : 104 : : 119 : 136
Verify the following:
108 : 72 : : 129 : 86
Verify the following:
39 : 65 : : 141 : 235
Find the value of x in each of the following proportions:
55 : 11 : : x : 6
Find the value of x in each of the following proportion:
27 : x : : 63 : 84
Find the value of x in each of the following proportions:
51 : 85 : : 57 : x
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
Write (T) for true and (F) for false in case of the following:
51 : 68 : : 85 : 102
True
False
Write (T) for true and (F) for false in case of the following:
36 : 45 : : 80 : 100
True
False
Write (T) for true and (F) for false in case of the following:
30 bags : 18 bags : : Rs 450 : Rs 270
True
False
Write (T) for true and (F) for false in case of the following:
81 kg : 45 kg : : 18 men : 10 men
True
False
Write (T) for true and (F) for false in case of the following:
45 km : 60 km : : 12 h : 15 h
True
False
Write (T) for true and (F) for false in case of the following:
32 kg : Rs 36 : : 8 kg : Rs 9
True
False
Determine if the following ratio form a proportion:
25 cm : 1 m and Rs 40 : Rs 160
Determine if the following ratio form a proportion:
39 litres : 65 litres and 6 bottles : 10 bottles
Determine if the following ratio form a proportion:
200 mL : 2.5 L and Rs 4 : Rs 50
Determine if the following ratio form a proportion:
2 kg : 80 kg and 25 g : 625 kg
In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108 respectively. Find the 3rd term.
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
Show that the following numbers are in continued proportion:
48, 60, 75
Show that the following numbers are in continued proportion:
36, 90, 225
Show that the following numbers are in continued proportion:
16, 84, 441
If 9, x, x 49 are in proportion, find the value of x.
An electric pole casts a shadow of length 20 m at a time when a tree 6 m high casts a shadow of length 8 m. Find the height of the pole.
Find the value of x if 5 : 3 : : x : 6.
R.S. Aggarwal solutions for Mathematics [English] Class 6 10 Ratio, Proportion and Unitary Method Exercise 10C [Pages 157 - 158]
If the cost of 14 m of cloth is Rs 1890, find the cost of 6 m of cloth.
If the cost of a dozen soaps is Rs 285.60, what will be the cost of 15 such soaps?
If 9 kg of rice costs Rs 327.60, what will be the cost of 50 kg of rice?
If 22.5 m of a uniform iron rod weighs 85.5 kg, what will be the weight of 5 m of the same rod?
If 15 tins of the same size contain 234 kg of oil, how much oil will there be in 10 such tins?
If 12 L of diesel is consumed by a car in covering a distance of 222 km, how many kilometers will it go in 22 L of diesel?
A transport company charges Rs 540 to carry 25 tonnes of weight. What will it charge to carry 35 tonnes?
4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?
35 inland letters cost Rs 87.50. How many such letters can we buy for 315?
The cost of 4 dozen bananas is Rs 104. How many bananas can be purchased for Rs 6.50?
The cost of 18 chairs is Rs 22770. How many such chairs can be bought for Rs 10120?
A car travels 195 km in 3 hours.
(i) How long will it take to travel 520 km?
(ii) How far will it travel in 7 hours at the same speed?
A labourer earns Rs 1980 in 12 days.
(i) How much does he earn in 7 days?
(ii) In how many days will he earn Rs 2640?
The weight of 65 books is 13 kg.
(i) What is the weight of 80 such books?
(ii) How many such books weigh 6.4 kg?
If 48 boxes contain 6000 pens, how many such boxes will be needed for 1875 pens?
24 workers can build a wall in 15 days. How many days will 9 workers take to build a similar wall?
40 men can finish a piece of work in 26 days. How many men will be needed to finish it in 16 days?
In an army camp, there were provisions for 550 men for 28 days. But, 700 men attended the camp. How long did the provisions last?
A given quantity of rice is sufficient for 60 persons for 3 days. How many days would the rice last for 18 persons?
R.S. Aggarwal solutions for Mathematics [English] Class 6 10 Ratio, Proportion and Unitary Method Exercise 10D [Page 158]
The ratio 92 : 115 in its simplest for is
23 : 25
18 : 23
3 : 5
4 : 5
If 57 : x : : 51 : 85, then the value of x is
95
76
114
none of these
If 25 : 35 : : 45 : x, then the value of x is
63
72
54
none of these
If 4 : 5 : : x : 35, then the value of x is
42
32
28
none of these
If a, b, c, d are in proportion, then
ac = bd
ad = bc
ab = cd
none of these
If a, b, c are in proportion, then
a2 = bc
b2 = ac
c2 = ab
none of these
Choose the correct statement:
(5 : 8) > (3 : 4)
(5 : 8) < (3 : 4)
two ratios cannot be compared
If Rs 760 is divided between A and B in the ratio 8 : 11, then B's share is
Rs 440
Rs 320
Rs 430
Rs 330
Two numbers are in the ratio 5 : 7 and the sum of these numbers is 252. The larger of these numbers is
85
119
105
147
The sides of a triangle are in the ratio 1 : 3 : 5 and its perimeter is 90 cm. The length of its largest side is
40 cm
50 cm
36 cm
54 cm
The ratio of boys and girls in a school is 12 : 5. If the number of girls is 840, the total strength of the school is
1190
2380
2856
2142
If the cost of 12 pens is Rs 138, then the cost of 14 such pens is
Rs 164
Rs 161
Rs 118.30
Rs 123.50
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
42 days
45 days
48 days
none of these
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
52
31
13
65
In covering 111 km, a car consumes 6 L of petrol. How many kilometers will it go to 10 L of petrol?
172 km
185 km
205 km
266.4 km
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
22 days
35`7/11` days
34 days
none of these
The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is
30°
60°
90°
120°
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
40 m
45 m
54 m
50 m
If a bus covers 195 km in 3 hours and a train covers 300 km in 4 hours, then the ratio of their speeds is
13 : 15
15 : 13
13 : 12
12 : 13
If the cost of 5 bars of soap is Rs 82.50, then the cost of one dozen such bars is
Rs 208
Rs 192
Rs 198
Rs 204
If the cost of 30 packets of 8 pencils each is Rs 600, what is the cost of 25 packets of 12 pencils each?
Rs 725
Rs 750
Rs 480
Rs 720
A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?
Rs 344
Rs 324
Rs 268.75
none of these
The 1st, 2nd, and 4th terms of a proportion are 12, 21, and 14 respectively. Its third term is
16
18
21
8
10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?
9 h 36 min
15 h
6 h 40 min
13 h 20 min
R.S. Aggarwal solutions for Mathematics [English] Class 6 10 Ratio, Proportion and Unitary Method Test Paper 10 [Page 161]
Find the ratio of:
90 cm to 1.05 m
Find the ratio of:
35 minutes to an hour
Find the ratio of:
150 mL to 2 L
Find the ratio of:
2 dozens to a score
The ratio of zinc and copper in an alloy is 7 : 9. If the weight of copper in the alloy is 12.6 kg, find the weight of zinc in it.
Divide Rs 1400 among A. B and C in the ratio 2 : 3 : 5.
Prove that (5 : 6) > (3 : 4).
40 men can finish a piece of work in 26 days. How many men will be needed to finish it in 16 days?
In an army camp, there were provisions for 425 men for 30 days. How long did the provisions last for 375 men?
Find the value of x when 36 : x : : x : 16.
Show that 48, 60, 75 are in continued proportion.
Two numbers are in the ratio 3 : 5 and their sum is 96. The larger number is
36
42
60
70
A car travels 288 km in 4 hours and a train travels 540 km in 6 hours. The ratio of their speeds is
5 : 4
4 : 5
5 : 6
3 : 5
Solutions for 10: Ratio, Proportion and Unitary Method
R.S. Aggarwal solutions for Mathematics [English] Class 6 chapter 10 - Ratio, Proportion and Unitary Method
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