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If (A - 2b - 3c + 4d)/(A + 2b - 3c - 4d) = (A - 2b + 3c - 4d)/(A + 2b + 3c + 4d) Show that 2ad = 3bc - ICSE Class 10 - Mathematics

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Question

If `(a - 2b - 3c + 4d)/(a + 2b - 3c - 4d) = (a - 2b + 3c - 4d)/(a + 2b + 3c + 4d)` show that 2ad = 3bc

Solution

`(a - 2b - 3c + 4d)/(a + 2b - 3c - 4d) = (a - 2b + 3c - 4d)/(a + 2b + 3c + 4d)`

Applying componendo and dividendo

`((a - 2b - 3 + 4d) + (a + 2b - 3c - 4d))/((a - 2b - 3c + 4d) - (a + 2b - 3c - 4d))`

`= ((a - 2b + 3c - 4d) + (a + 2b = 3c + 4d))/((a - 2b + 3c - 4d) - (a + 3b + 3c + 4d))`

`(2(a - 3c))/(2(-2b + 4d)) = (2(a + 3c))/(2(-2b - 4d))`

`(a - 3c)/(a + 3c) = (-2b + 4d)/(-2b - 4d)`

Applying componendo and dividendo

`(a - 3c + a + 3c)/(a - 3c - a - 3c) = (-2b + 4d - 2b - 4d)/(-2b + 4d + 2b + 4d)`

`(2a)/(-6c) = (-4b)/(8d)`

`a/(-3c) = (-b)/(2d)`

2ad = 3bc

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 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: 8

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Solution If (A - 2b - 3c + 4d)/(A + 2b - 3c - 4d) = (A - 2b + 3c - 4d)/(A + 2b + 3c + 4d) Show that 2ad = 3bc Concept: Componendo and Dividendo Properties.
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