Question

The three number are in the ratio 3:7:9. if 5 is subtracted from the second , the resulting number from A.P. Find the original numbers.

Answer 1

» Let's the number are 3x, 7x and 9x.
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Now

» According to the question :-

» 3x, 7x-5 and 9x are in AP.

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Let's

$= > t _{1} = 3x \\ \\ = > t _{2} = 7x - 5 \\ \\ = > t _{3} = 9x$
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» then we know that in AP

$= > t _{2} - t _{1} = t _{3} - t _{2} \\ \\ = > 7x - 5 - 3x = 9x - 7x + 5 \\ \\ = > 4x - 5 = 2x + 5 \\ \\ = > 2x = 10 \\ \\ = > x = 5$
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» Hence the number are :-

=> 3x = 3×5 = 15
=> 7x = 7×5 = 35
=> 9x = 9×5 = 45
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