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Question
Find two numbers in the ratio of 8 : 7 such that when each is decreased by , they are in the ratio 11 : 9.
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Solution
The ratio is 8 : 7
Let the numbers be 8x and 7x,
According to condition,
`(8x - 25/2)/(7x - 25/2) = (11)/(9)`
⇒ `(16x - 25/2)/(14x - 25/2) = (11)/(9)`
⇒ `((16x - 25) xx 2)/(2(14x - 25)) = (11)/(9)`
⇒ 154x – 275 = 144x – 225
⇒ 154x – 144x = 275 – 225
⇒ 10x = 50
∴ x = `(50)/(10)` = 5
∴ Numbers are 8x = 8 x 5 = 40
and 7x = 7 x 5 = 35.
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