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Areas of Different Plane Figures

Four points a...

Question

Four points are on a line segment If AB : BC = 1 : 2 and BC : CD = 8 : 5 then AB : BD equals

A

4 : 13

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B

1 : 13

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C

1 : 7

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D

3 : 13

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Solution

The correct option is A $4 : 13$
$G i v e n - A, B, C & D a r e c o l l i n e a r p o i n t s . A B : B C = 1 : 2, B C : C D = 8 : 5. T o f i n d o u t - A B : B D = ? S o l u t i o n - L e t u s a s s u m e A B = x a n d B C = 2 x s i n c e A B : B C = 1 : 2. N o w B C : C D = 8 : 5 = 2 : \frac{5}{4} . ∴ B C = 2 x a n d C D = \frac{5 x}{4} . S o B D = B C + C D = 2 x + \frac{5 x}{4} = \frac{13 x}{4} . ∴ S o A B : B D = x : \frac{13 x}{4} = 4 x : 13 x = 4 : 13. A n s - O p t i o n A .$

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