S Chand ICSE Class 10 Maths Chapter 6 Ratio Proportion Exercise 6C Solutions

Hi students, Welcome to Amans Maths Blogs (AMB). In this post, you will get S Chand ICSE Class 10 Maths Chapter 6 Ratio Proportion Exercise 6C Solutions. This is the chapter of introduction of ‘Ratio and Proportion‘ included in ICSE Class 10 Maths syllabus.

S Chand ICSE Maths Solutions Class 10 Chapter 6 Ratio Proportion Exercise 6C

S Chand ICSE Class 10 Maths Chapter 6 Ratio Proportion Exercise 6C: Ques No 1

If x/a = y/b = z/c, show that

(i) x³/a³ – y³/b³ + z³/c³ = xyz/abc

(ii) ((a²x² + b²y² + c²z²) / (a³x + b³y + c³z))^3/2 = √(xyz / abc)

(iii) (xz + ac) / (xz – ac) = (yz + bc) / (yz – dc)

S Chand ICSE Maths Solutions 1(i):

S Chand ICSE Maths Solutions 1(ii):

S Chand ICSE Maths Solutions 1(iii):

Ques No 2

If a/b = c/d = e/f, prove the following

(i) (pa³ + qc³ + re³) / (pb³ + qd³ + rf³) = ace/bdf

(ii) √((a⁴ + c⁴) / (b⁴ + d⁴)) = (pa² + qc²) / (pb² + qd²)

Solutions 2(i):

Solutions 2(ii):

Ques No 3

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

(i) (a + b + c)(a – b + c) = a² + b² + c²

(ii) (a² + b²) / (b² + c²) = a / c

(iii) (a³ + b³ + c³) / a²b²c² = 1/a³ + 1/b³ + 1/c³

Solutions 3(i):

Solutions 3(ii):

Solutions 3(iii):

Ques No 4

If a, b, c, d are in continued proportion, then prove that

(i) (b – c)² + (c – a)² + (d – b)² = (a – d)²

(ii) √[(a⁵ + b²c² + a³c²) / (b⁴c + d⁴ + b²cd²) = a / d

(iii) √ab – √bc + √cd = √((a – b + c)(b – c + d))

(iv) (3a + 5d) / (5a + 7d) =  (3a³ + 5d³) / (5a³ + 7d³)

Solutions 4(i):

Solutions 4(ii):

Solutions 4(iii):

Solutions 4(iv):

Ques No 5

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

Solutions:

Ques No 6

If x/(b + c – a) = y/(c + a – b) = z/(a + b – c), then show that each ratio is equal to (x + y + z) / (a + b + c).

Solutions:

Ques No 7

If a/(b + c) = b/(c + a) = c/(a + b), then prove that a(b – c) + b(c – a) + c(a – b) = 0

Solutions:

S Chand ICSE Class 10 Maths Chapter 6 Ratio Proportion Exercise 6C: Ques No 8

If ax = by = cz, then prove that x²/yz + y²/zx + z²/xy = bc/a² + ca/b² + ab/c².

S Chand ICSE Maths Solutions: