## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Ratio and Proportion Ex 7.2

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Ratio and Proportion Ex 7.2

Question 1.

Find the value of x in the following proportions:

(i) 10 : 35 = x : 42

(ii) 3 : x = 24 : 2

(iii) 2.5 : 1.5 = x : 3

(iv) x : 50 :: 3 : 2

Solution:

Question 2.

Find the fourth proportional to

(i) 3, 12, 15

(ii) \(\frac { 1 }{ 3 } ,\frac { 1 }{ 4 } ,\frac { 1 }{ 5 } \)

(iii) 1.5, 2.5, 4.5

(iv) 9.6 kg, 7.2 kg, 28.8 kg

Solution:

Question 3.

Find the third proportional to

(i) 5, 10

(ii) 0.24, 0.6

(iii) Rs. 3, Rs. 12

(iv) \(5 \frac { 1 }{ 4 } \) and 7.

Solution:

Question 4.

Find the mean proportion of:

(i) 5 and 80

(ii) \(\\ \frac { 1 }{ 12 } \) and \(\\ \frac { 1 }{ 75 } \)

(iii) 8.1 and 2.5

(iv) (a – b) and (a³ – a²b), a> b

Solution:

Question 5.

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

Solution:

Question 6.

What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion? (2009)

Solution:

Question 7.

What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion? (2004)

Solution:

Question 8.

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

Solution:

Question 9.

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

Solution:

Question 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?

Solution:

Question 11.

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

Solution:

Question 12.

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

Solution:

Question 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).

Solution:

Question 14.

If y is mean proportional between x and z, prove that

xyz (x + y + z)³ = (xy + yz + zx)³.

Solution:

Question 15.

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

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

If ax = by = cz; prove that

\(\frac { { x }^{ 2 } }{ yz } +\frac { { y }^{ 2 } }{ zx } +\frac { { z }^{ 2 } }{ xy } \) = \(\frac { bc }{ { a }^{ 2 } } +\frac { ca }{ { b }^{ 2 } } +\frac { ab }{ { c }^{ 2 } } \)

Solution:

Question 19.

Solution:

Question 20.

If x, y, z are in continued proportion, prove that:\(\frac { { \left( x+y \right) }^{ 2 } }{ { \left( y+z \right) }^{ 2 } } =\frac { x }{ z } \). (2010)

Solution:

Question 21.

If a, b, c are in continued proportion, prove that:

\(\frac { { pa }^{ 2 }+qab+{ rb }^{ 2 } }{ { pb }^{ 2 }+qbc+{ rc }^{ 2 } } =\frac { a }{ c } \)

Solution:

Question 22.

Solution:

Question 23.

Solution: