In the figure $D F ∥ A G, D E ∥ A B, A B = 15, C D = 8, A D = x, D E = 10, F G = y$ and $C G = 6$ . The ratio $x : y$ is equal to :

1 : 2

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1 : 3

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2 : 1

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3 : 2

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Solution

The correct option is C $2 : 1$
$G i v e n : D F ∥ A G, D E ∥ A B, A B = 15, C D = 8, A D = x, D E = 10, F G = y a n d C G = 6 C F = 6 - y a n d A C = 8 + x I n △ C A B \frac{C D}{A C} = \frac{D E}{A B} (B a s i c P r o p o r t i n a l i t y t h e o r m) \frac{8}{8 + x} = \frac{10}{15} 120 = 80 + 10 x \Rightarrow 40 = 10 x \Rightarrow x = 4.... (1) I n △ A G C, D F ∥ A G H e n c e \frac{C D}{D A} = \frac{C F}{F G} \Rightarrow \frac{8}{x} = \frac{6 - y}{y} \Rightarrow \frac{8}{4} = \frac{6 - y}{y} \Rightarrow 2 y = 6 - y \Rightarrow 3 y = 6 \Rightarrow y = 2 H e n c e r a t i o o f x : y = 4 : 2 = 2 : 1 O p t i o n (C) i s c o r e c t a n s w e r$

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D F ∥ A G, D E ∥ A B, A B = 15, C D = 8, A D = x, D E = 10, F G = y

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