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# If a : B = C : D, Prove That: (6a + 7b) (3c – 4d) = (6c + 7d) (3a – 4b). - ICSE Class 10 - Mathematics

ConceptComponendo and Dividendo Properties

#### Question

If a : b = c : d, prove that: (6a + 7b) (3c – 4d) = (6c + 7d) (3a – 4b).

#### Solution

Given a/b = c/d

=> (6a)/(7b) = (6c)/(7d)   (Multiplying each side by 6/7)

=> (6a + 7b)/(7b) = (6c + 7d)/(7d)  (By componendo)

=> (6a + 7b)/(6c + 7d) = (7b)/(7d) = b/d .....(1)

Also a/b = c/d

=> (3a)/(4b) = (3c)/(4d)     (Mutipling each side by 3/4)

=> (3a - 4b)/(4b) = (3c - 4d)/(4d)   (By dividendo)

=>(3a - 4b)/(4b) = (3c - 4d)/(4d) (By dividendo)

=> (3a - 4b)/(3c - 4d) = (4b)/(4d) =  b/d  ....(2)

From (1) and (2)

(6a + 7b)/(6c + 7d) = (3a - 4b)/(3c - 4c)

(6a+ 7b)(3c - 4d) = (6c + 7d)(3a - 4b)

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#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7C | Q: 2

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Solution If a : B = C : D, Prove That: (6a + 7b) (3c – 4d) = (6c + 7d) (3a – 4b). Concept: Componendo and Dividendo Properties.
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