ML Aggarwal solutions for Understanding ICSE Mathematics Class 10 Solved chapter 7 - Ratio and Proportion [Latest edition]

Chapters

Chapter 2: Banking

Chapter 3: Shares and Dividends

Chapter 4: Linear Inequations

Chapter 5: Quadratic Equations in One Variable

Chapter 6: Factorization

Chapter 7: Ratio and Proportion

Chapter 8: Matrices

Chapter 9: Arithmetic and Geometric Progressions

Chapter 10: Reflection

Chapter 11: Section Formula

Chapter 12: Equation of a Straight Line

Chapter 13: Similarity

Chapter 14: Locus

Chapter 15: Circles

Chapter 16: Constructions

Chapter 17: Mensuration

Chapter 18: Trigonometric Identities

Chapter 19: Trigonometric Tables

Chapter 20: Heights and Distances

Chapter 21: Measures of Central Tendency

Chapter 22: Probability

Chapter 7: Ratio and Proportion

Exercise 7.1Exercise 7.2Exercise 7.3Multiple Choice QuestionChapter Test
Exercise 7.1

ML Aggarwal solutions for Understanding ICSE Mathematics Class 10 Solved Chapter 7 Ratio and Proportion Exercise 7.1

Exercise 7.1 | Q 1

An alloy consists of 27(1)/(2) kg of copper and 2(3)/(4) kg of tin. Find the ratio by weight of tin to the alloy

Exercise 7.1 | Q 2.1

Find the compounded ratio of: 2 : 3 and 4 : 9

Exercise 7.1 | Q 2.2

Find the compounded ratio of: 4 : 5, 5 : 7 and 9 : 11

Exercise 7.1 | Q 2.3

Find the compounded ratio of: (a – b) : (a + b), (a + b)2 : (a2 + b2) and (a4 – b4) : (a2 – b2)2

Exercise 7.1 | Q 3.1

Find the duplicate ratio of 2 : 3

Exercise 7.1 | Q 3.2

Find the duplicate ratio of sqrt(5) : 7

Exercise 7.1 | Q 3.3

Find the duplicate ratio of 5a : 6b

Exercise 7.1 | Q 4.1

Find the triplicate ratio of 3 : 4

Exercise 7.1 | Q 4.2

Find the triplicate ratio of (1)/(2) : (1)/(3)

Exercise 7.1 | Q 4.3

Find the triplicate ratio of 13 : 23

Exercise 7.1 | Q 5.1

Find the sub-duplicate ratio of 9 : 16

Exercise 7.1 | Q 5.2

Find the sub-duplicate ratio of (1)/(4) : (1)/(9)

Exercise 7.1 | Q 5.3

Find the sub-duplicate ratio of 9a2 : 49b2

Exercise 7.1 | Q 6.1

Find the sub-triplicate ratio of 1 : 216

Exercise 7.1 | Q 6.2

Find the sub-triplicate ratio of (1)/(8) : (1)/(125)

Exercise 7.1 | Q 6.3

Find the sub-triplicate ratio of 27a3 : 64b3

Exercise 7.1 | Q 7.1

Find the reciprocal ratio of 4 : 7

Exercise 7.1 | Q 7.2

Find the reciprocal ratio of 32 : 42

Exercise 7.1 | Q 7.3

Find the reciprocal ratio of (1)/(9) : 2

Exercise 7.1 | Q 8

Arrange the following ratios in ascending order of magnitude: 2 : 3, 17 : 21, 11 : 14 and 5 : 7

Exercise 7.1 | Q 9.1

If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, find A : D

Exercise 7.1 | Q 9.2

If x : y = 2 : 3, and y : z = 4 : 7, find x : y : z

Exercise 7.1 | Q 10.1

If A: B = (1)/(4) : (1)/(5) and B : C = (1)/(7) : (1)/(6), find A : B : C.

Exercise 7.1 | Q 10.2

If 3A = 4B = 6C, find A : B : C

Exercise 7.1 | Q 11.1

If (3x + 5y)/(3x - 5y) = (7)/(3) , Find x : y

Exercise 7.1 | Q 11.2

If a : b = 3 : 11, find (15a – 3b) : (9a + 5b). a

Exercise 7.1 | Q 12.1

If (4x² + xy) : (3xy – y²) = 12 : 5, find (x + 2y) : (2x + y).

Exercise 7.1 | Q 12.2

If y (3x – y) : x (4x + y) = 5 : 12. Find (x² + y²) : (x + y)².

Exercise 7.1 | Q 13.1

If (x – 9) : (3x + 6) is the duplicate ratio of 4 : 9, find the value of x.

Exercise 7.1 | Q 13.2

If (3x + 1) : (5x + 3) is the triplicate ratio of 3 : 4, find the value of x.

Exercise 7.1 | Q 13.3

If (x + 2y) : (2x – y) is equal to the duplicate ratio of 3 : 2, find x : y.

Exercise 7.1 | Q 14.1

Find two numbers in the ratio of 8 : 7 such that when each is decreased by , they are in the ratio 11 : 9.

Exercise 7.1 | Q 14.2

The income of a man is increased in the ratio of 10 : 11. If the increase in his income is Rs 600 per month, find his new income.

Exercise 7.1 | Q 15.1

A woman reduces her weight in the ratio 7 : 5. What does her weight become if originally it was 91 kg.

Exercise 7.1 | Q 15.2

A school collected Rs 2100 for charity. It was decided to divide the money between an orphanage and a blind school in the ratio of 3 : 4. How much money did each receive?

Exercise 7.1 | Q 16.1

The sides of a triangle are in the ratio 7 : 5 : 3 and its perimeter is 30 cm. Find the lengths of sides.

Exercise 7.1 | Q 16.2

If the angles of a triangle are in the ratio 2 : 3 : 4, find the angles.

Exercise 7.1 | Q 17

Three numbers are in the ratio (1)/(2) : (1)/(3) : (1)/(4) If the sum of their squares is 244, find the numbers.

Exercise 7.1 | Q 18.1

A certain sum was divided among A, B and C in the ratio 7 : 5 : 4. If B got Rs 500 more than C, find the total sum divided.

Exercise 7.1 | Q 18.2

In a business, A invests Rs 50000 for 6 months, B Rs 60000 for 4 months and C, Rs 80000 for 5 months. If they together earn Rs 18800 find the share of each.

Exercise 7.1 | Q 19.1

In a mixture of 45 litres, the ratio of milk to water is 13 : 2. How much water must be added to this mixture to make the ratio of milk to water as 3 : 1 ?

Exercise 7.1 | Q 19.2

The ratio of the number of boys to the number of girls in a school of 560 pupils is 5 : 3. If 10 new boys are admitted, find how many new girls may be admitted so that the ratio of the number of boys to the number of girls may change to 3 : 2.

Exercise 7.1 | Q 20.1

The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7. Their expenditures are in the ratio 3:5. If each saves Rs. 80 every month, find their monthly pocket money.

Exercise 7.1 | Q 20.2

In class X of a school, the ratio of the number of boys to that of the girls is 4 : 3. If there were 20 more boys and 12 less girls, then the ratio would have been 2 : 1, How many students were there in the class?

Exercise 7.1 | Q 21

In an examination, the ratio of passes to failures was 4 : 1. If 30 less had appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1. How many students appeared for the examination

Exercise 7.2

ML Aggarwal solutions for Understanding ICSE Mathematics Class 10 Solved Chapter 7 Ratio and Proportion Exercise 7.2

Exercise 7.2 | Q 1.1

Find the value of x in the following proportions : 10 : 35 = x : 42

Exercise 7.2 | Q 1.2

Find the value of x in the following proportions : 3 : x = 24 : 2

Exercise 7.2 | Q 1.3

Find the value of x in the following proportions : 2.5 : 1.5 = x : 3

Exercise 7.2 | Q 1.4

Find the value of x in the following proportions : x : 50 :: 3 : 2

Exercise 7.2 | Q 2.1

Find the fourth proportional to 3, 12, 15

Exercise 7.2 | Q 2.2

Find the fourth proportional to (1)/(3), (1)/(4), (1)/(5)

Exercise 7.2 | Q 2.3

Find the fourth proportional to 1.5, 2.5, 4.5

Exercise 7.2 | Q 2.4

Find the fourth proportional to 9.6 kg, 7.2 kg, 28.8 kg

Exercise 7.2 | Q 3.1

Find the third proportional to 5, 10

Exercise 7.2 | Q 3.2

Find the third proportional to 0.24, 0.6

Exercise 7.2 | Q 3.3

Find the third proportional to Rs. 3, Rs. 12

Exercise 7.2 | Q 3.4

Find the third proportional to 5(1)/(4) and 7.

Exercise 7.2 | Q 4.1

Find the mean proportion of: 5 and 80

Exercise 7.2 | Q 4.2

Find the mean proportion of: (1)/(12) and (1)/(75)

Exercise 7.2 | Q 4.3

Find the mean proportion of: 8.1 and 2.5

Exercise 7.2 | Q 4.4

Find the mean proportion of: (a – b) and (a³ – a²b), a> b

Exercise 7.2 | Q 5

If a, 12, 16 and b are in continued proportion find a and b.

Exercise 7.2 | Q 6

What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?

Exercise 7.2 | Q 7

What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?

Exercise 7.2 | Q 8

If 2x – 1, 5x – 6, 6x + 2 and 15x – 9 are in proportion, find the value of x.

Exercise 7.2 | Q 9

If x + 5 is the mean proportion between x + 2 and x + 9, find the value of x.

Exercise 7.2 | Q 10

What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?

Exercise 7.2 | Q 11

Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.

Exercise 7.2 | Q 12

If b is the mean proportional between a and c, prove that a, c, a² + b², and b² + c² are proportional.

Exercise 7.2 | Q 13

If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).

Exercise 7.2 | Q 14

If y is mean proportional between x and z, prove that
xyz (x + y + z)³ = (xy + yz + zx)³.

Exercise 7.2 | Q 15

If a + c = mb and (1)/b + (1)/d = m/c, prove that a, b, c and d are in proportion.

Exercise 7.2 | Q 16.1

If x/a = y/b = z/c, prove that x^3/a^2 + y^3/b^2 + z^3/c^2 = (x+ y+ z)^3/(a + b+ c)^2

Exercise 7.2 | Q 16.2

If x/a = y/b = z/c, prove that [(a^2x^2 + b^2y^2 + c^2z^2)/(a^2x + b^3y +c^3z)]^3 = "xyz"/"abc"

Exercise 7.2 | Q 16.3

If x/a = y/b = z/c, prove that "ax - by"/((a + b)(x- y)) + "by - cz"/((b + c)(y - z)) + "cz - ax"/((c + a)(z - x) = 3

Exercise 7.2 | Q 17.1

If a/c = c/d = c/f prove that : (b2 + d2 + f2) (a2 + c2 + e2) = (ab + cd + ef)

Exercise 7.2 | Q 17.2

If a/c = c/d = c/f prove that : (a^3 + c^3)^2/(b^3 + d^3)^2 = e^6/f^6

Exercise 7.2 | Q 17.3

If a/c = c/d = c/f prove that : (a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"

Exercise 7.2 | Q 17.4

If a/c = c/d = c/f prove that : bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3 = 27(a + b)(c + d)(e + f)

Exercise 7.2 | Q 18

If ax = by = cz; prove that x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2

Exercise 7.2 | Q 19.1

If a, b, c and d are in proportion, prove that: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b)

Exercise 7.2 | Q 19.2

If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d

Exercise 7.2 | Q 19.3

If a, b, c and d are in proportion, prove that: (a4 + c4) : (b4 + d4) = a2 c2 : b2 d2.

Exercise 7.2 | Q 19.4

If a, b, c and d are in proportion, prove that: (a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)

Exercise 7.2 | Q 19.5

If a, b, c and d are in proportion, prove that: (a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)

Exercise 7.2 | Q 19.6

If a, b, c and d are in proportion, prove that: (a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)

Exercise 7.2 | Q 19.7

If a, b, c and d are in proportion, prove that: (a^2 + b^2)/(c^2 + d^2) = "ab + ad - bc"/"bc + cd - ad"

Exercise 7.2 | Q 19.8

If a, b, c and d are in proportion, prove that: abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2] = a2 + b2 + c2 + d

Exercise 7.2 | Q 20

If x, y, z are in continued proportion, prove that: (x + y)^2/(y + z)^2 = x/z.

Exercise 7.2 | Q 21

If a, b, c are in continued proportion, prove that: (pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c

Exercise 7.2 | Q 22.1

If a, b, c are in continued proportion, prove that: "a + b"/"b + c" = (a^2(b - c))/(b^2(a - b)

Exercise 7.2 | Q 22.2

If a, b, c are in continued proportion, prove that: (1)/a^3 + (1)/b^3 + (1)/c^3 = a/(b^2c^2) + b/(c^2a^2) + c/(a^2b^2)

Exercise 7.2 | Q 22.3

If a, b, c are in continued proportion, prove that: a : c = (a2 + b2) : (b2 + c2)

Exercise 7.2 | Q 22.4

If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4)

Exercise 7.2 | Q 22.5

If a, b, c are in continued proportion, prove that: abc(a + b + c)3 = (ab + bc + ca)3

Exercise 7.2 | Q 22.6

If a, b, c are in continued proportion, prove that: (a + b + c) (a – b + c) = a2 + b2 + c2

Exercise 7.2 | Q 23.1

If a, b, c, d are in continued proportion, prove that: (a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d

Exercise 7.2 | Q 23.2

If a, b, c, d are in continued proportion, prove that: (a2 – b2) (c2 – d2) = (b2 – c2)2

Exercise 7.2 | Q 23.3

If a, b, c, d are in continued proportion, prove that: (a + d)(b + c) – (a + c)(b + d) = (b – c)2

Exercise 7.2 | Q 23.4

If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)

Exercise 7.2 | Q 23.5

If a, b, c, d are in continued proportion, prove that: ((a -b)/c + (a - c)/b)^2 - ((d - b)/c + (d - c)/b)^2 = (a - d)^2 (1/c^2 - 1/b^2)

Exercise 7.3

ML Aggarwal solutions for Understanding ICSE Mathematics Class 10 Solved Chapter 7 Ratio and Proportion Exercise 7.3

Exercise 7.3 | Q 1.1

If a : b : : c : d, prove that (2a +5b)/(2a - 5b) = (2c + 5d)/(2c - 5d)

Exercise 7.3 | Q 1.2

If a : b : : c : d, prove that (5a + 11b)/(5c + 11d) = (5a - 11b)/(5c - 11d)

Exercise 7.3 | Q 1.3

If a : b : : c : d, prove that (2a + 3b)(2c – 3d) = (2a – 3b)(2c + 3d)

Exercise 7.3 | Q 1.4

If a : b : : c : d, prove that (la + mb) : (lc + mb) :: (la – mb) : (lc – mb)

Exercise 7.3 | Q 2.1

If (5x + 7y)/(5u + 7v) = (5x - 7y)/(5u - 7v), show that x/y = u/v

Exercise 7.3 | Q 2.2

If (8a - 5b)/(8c - 5a) = (8a + 5b)/(8c + 5d), prove that a/b = c/d

Exercise 7.3 | Q 3

If (4a + 5b) (4c – 5d) = (4a – 5d) (4c + 5d), prove that a, b, c, d are in proporton.

Exercise 7.3 | Q 4

If (pa + qb) : (pc + qd) :: (pa – qb) : (pc – qd) prove that a : b : : c : d

Exercise 7.3 | Q 5

If (ma + nb): b :: (mc + nd) : d, prove that a, b, c, d are in proportion.

Exercise 7.3 | Q 6

If (11a² + 13b²) (11c² – 13d²) = (11a² – 13b²)(11c² + 13d²), prove that a : b :: c : d.

Exercise 7.3 | Q 7

If (a + 3b + 2c + 6d) (a – 3b – 2c + 6d) = (a + 3b – 2c – 6d) (a – 3b + 2c – 6d), prove that a : b :: c : d.

Exercise 7.3 | Q 8

If x = (2a + b)/(a + b) find the value of (x + a)/(x - a) + (x + b)/(x - b)

Exercise 7.3 | Q 9

If x = (8ab)/"a + b" find the value of (x + 4a)/(x - 4a) + (x + 4b)/(x - 4b)

Exercise 7.3 | Q 10

If x = (4sqrt(6))/(sqrt(2) + sqrt(3) find the value of (x + 2sqrt(2))/(x - 2sqrt(2)) + (x + 2sqrt(3))/(x - 2sqrt(3)

Exercise 7.3 | Q 11

Solve x : (sqrt(36x + 1) + 6sqrt(x))/(sqrt(36x + 1) -6sqrt(x)) = 9

Exercise 7.3 | Q 12.1

Find x from the following equations : (sqrt(2 - x) + sqrt(2 + x))/(sqrt(2 - x) - sqrt(2 + x) = 3

Exercise 7.3 | Q 12.2

Find x from the following equations : (sqrt(x + 4) + sqrt(x - 10))/(sqrt(x + 4) - sqrt(x - 10)) = (5)/(2)

Exercise 7.3 | Q 12.3

Find x from the following equations : (sqrt(1 + x) + sqrt(1 - x))/(sqrt(1 + x) - sqrt(1 - x)) = a/b

Exercise 7.3 | Q 12.4

Find x from the following equations : (sqrt(12x + 1) + sqrt(2x - 3))/(sqrt(12x + 1) - sqrt(2x - 3)) = (3)/(2)

Exercise 7.3 | Q 12.5

Find x from the following equations : (3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = (5)/(1)

Exercise 7.3 | Q 12.6

Find x from the following equations : (sqrt(a + x) + sqrt(a - x))/(sqrt(a + x) - sqrt(a - x)) = c/d

Exercise 7.3 | Q 13

Solve (1 + x + x^2)/(1 - x + x^2) = (62(1 +x))/(63(1 + x)

Exercise 7.3 | Q 14

Solve for x : 16((a - x)/(a + x))^3 = (a + x)/(a - x)

Exercise 7.3 | Q 15

If x = (sqrt(a + x) + sqrt(a - 1))/(sqrt(a + 1 - sqrt(a - 1), using properties of proportion , show that x2 – 2ax + 1 = 0

Exercise 7.3 | Q 16

Given x = (sqrt(a^2 + b^2) + sqrt(a^2 - b^2))/(sqrt(^2 + b^2) - sqrt(a^2 - b^2) Use componendo and dividendo to prove that b2 = (2a^2x)/(x^2 + 1)

Exercise 7.3 | Q 17

Given that (a^3 + 3ab^2)/(b^3 + 3a^2b) = (63)/(62). Using componendo and dividendo find a: b.

Exercise 7.3 | Q 18

Give (x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27) Using componendo and dividendo find x : y.

Exercise 7.3 | Q 19

Using the properties of proportion, solve the following equation for x; given (x^3 + 3x)/(3x^2 + 1) = (341)/(91)

Exercise 7.3 | Q 20

If (x + y)/(ax + by) = (y + z)/(ay + bz) = (z + x)/(az + bx), prove that each of these ratio is equal to (2)/(a + b) unless x + y + z = 0

Multiple Choice Question

ML Aggarwal solutions for Understanding ICSE Mathematics Class 10 Solved Chapter 7 Ratio and Proportion Multiple Choice Question

Multiple Choice Question | Q 1

Choose the correct answer from the given options :

The ratio of 45 minutes to 5(3)/(4) hours is

• 180:23

• 3:23

• 23:3

• 6:23

Multiple Choice Question | Q 2

Choose the correct answer from the given options :

The ratio of 4 litres to 900 mL is

• 4 : 9

• 40 : 9

• 9 : 40

• 20 : 9

Multiple Choice Question | Q 3

Choose the correct answer from the given options :

When the number 210 is increased in the ratio 5 : 7, the new number is

• 150

• 180

• 294

• 420

Multiple Choice Question | Q 4

Choose the correct answer from the given options :

Two numbers are in the ratio 7 : 9. If the sum of the numbers is 288, then the smaller number is

• 126

• 162

• 112

• 144

Multiple Choice Question | Q 5

Choose the correct answer from the given options :

A ratio equivalent to the ratio (2)/(3) : (5)/(7) is

• 4:6

• 5:7

• 15:14

• 14:15

Multiple Choice Question | Q 6

Choose the correct answer from the given options :

The ratio of number of edges of a cube to the number of its faces is

• 2 : 1

• 1 : 2

• 3 : 8

• 8 : 3

Multiple Choice Question | Q 7

Choose the correct answer from the given options :

If x, 12, 8 and 32 are in proportion, then the value of x is

• 6

• 4

• 3

• 2

Multiple Choice Question | Q 8

Choose the correct answer from the given options :

The fourth proportional to 3, 4, 5 is

• 6

• (20)/(3)

• (15)/(4)

• (12)/(5)

Multiple Choice Question | Q 9

Choose the correct answer from the given options :

The third proportional to 6(1)/(4) and 5 is

• 4

• 8(1)/(2)

• 3

• none of these

Multiple Choice Question | Q 10

Choose the correct answer from the given options :

The mean proportional between (1)/(2) and 128 is

• 64

• 32

• 16

• 8

Chapter Test

ML Aggarwal solutions for Understanding ICSE Mathematics Class 10 Solved Chapter 7 Ratio and Proportion Chapter Test

Chapter Test | Q 1

Find the compound ratio of:
(a + b)2 : (a – b )2 ,
(a2 – b2) : (a2 + b2),
(a4 – b4) : (a + b)4

Chapter Test | Q 2

If (7 p + 3 q) : (3 p – 2 q) = 43 : 2 find p : q

Chapter Test | Q 3

If a : b = 3 : 5, find (3a + 5b): (7a – 2b).

Chapter Test | Q 4

The ratio of the shorter sides of a right angled triangle is 5 : 12. If the perimeter of the triangle is 360 cm, find the length of the longest side.

Chapter Test | Q 5

The ratio of the pocket money saved by Lokesh and his sister is 5 : 6. If the sister saves Rs 30 more, how much more the brother should save in order to keep the ratio of their savings unchanged?

Chapter Test | Q 6

In an examination, the number of those who passed and the number of those who failed were in the ratio of 3 : 1. Had 8 more appeared, and 6 less passed, the ratio of passed to failures would have been 2 : 1. Find the number of candidates who appeared.

Chapter Test | Q 7

What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?

Chapter Test | Q 8

If (a + 2 b + c), (a – c) and (a – 2 b + c) are in continued proportion, prove that b is the mean proportional between a and c.

Chapter Test | Q 9

If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.

Chapter Test | Q 10

If a, b, c, d, e are in continued proportion, prove that: a : e = a4 : b4.

Chapter Test | Q 11

Find two numbers whose mean proportional is 16 and the third proportional is 128.

Chapter Test | Q 12

If q is the mean proportional between p and r, prove that: p3 – 3q2 + r2 = q^4(1/p^2 - 3/q^2 + 1/r^2)

Chapter Test | Q 13.1

If a/b = c/d = c/f, prove that each ratio is sqrt((3a^2 - 5c^2 + 7e^2)/(3b^2 - 5d^2 + 7f^2)

Chapter Test | Q 13.2

If a/b = c/d = e/f, prove that each ratio is [(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)

Chapter Test | Q 14

If x/a = y/b = z/c, prove that (3x^3 - 5y^3 + 4c^3)/(3a^3 - 5b^3 + 4c^3) = ((3x - 5y + 4c)/(3a - 5b + ac))^3

Chapter Test | Q 15

If x : a = y : b, prove that (x^4 + a^4)/(x^3 + a^3) + (y^4 + b^4)/(y^3 + b^3) = ((x + y)^4 + (a + b)^4)/((x+ y)^3 + (a + b)^3

Chapter Test | Q 16

If x/(b + c - a) = y/(c + a - b) = z/(a + b - c)  prove that each ratio’s equal to : (x + y + z)/(a + b + c)

Chapter Test | Q 17.1

If a : b = 9 : 10, find the value of (5a + 3b)/(5a - 3b)

Chapter Test | Q 17.2

If a : b = 9 : 10, find the value of (2a^2 - 3b^2)/(2a^2 + 3b^2)

Chapter Test | Q 18

If (3x² + 2y²) : (3x² – 2y²) = 11 : 9, find the value of (3x^4 + 5y^4)/(3x^4 - 5y^4)

Chapter Test | Q 19

If x = (2mab)/(a + b), find the value of (x + ma)/(x - ma) + (x + mb)/(x - mb)

Chapter Test | Q 20

If x = "pab"/(a + b), provee that (x + pa)/(x - pa) - (x + pb)/(x - pb) = (2(a^2 - b^2))/(ab)

Chapter Test | Q 21

Find x from the equation (a+ x + sqrt(a^2  x^2))/(a + x - sqrt(a^2 - x^2)) = b/x

Chapter Test | Q 22

If x = (root(3)(a + 1) + root(3)(a - 1))/(root(3)(a + 1) - root(3)(a - 1),prove that :
x³ – 3ax² + 3x – a = 0

Chapter Test | Q 23

If (by + cz)/(b^2 + c^2) = (cz + ax)/(c^2 + a^2) = (ax + by)/(a^2 + b^2), prove that each of these ratio is equal to x/a = y/b = z/c

Chapter 7: Ratio and Proportion

Exercise 7.1Exercise 7.2Exercise 7.3Multiple Choice QuestionChapter Test

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Concepts covered in Understanding ICSE Mathematics Class 10 Solved chapter 7 Ratio and Proportion are Concept of Ratio, Concept of Proportion, Componendo and Dividendo Properties, Alternendo and Invertendo Properties, Direct Applications, Concept of Ratio.

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