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If $x : y = 8 : 9,$ then what is the ratio $(7 x − 4 y) : 3 x + 2 y$ ?

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10 : 27

90 : 21

10 : 21

10 : 25

answer is C.

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Detailed Solution

Given,

x : y = 8 : 9

Then,

x y = 89

⇒

x = 8 y 9

The given ratio is,

7 x − 4 y 3 x + 2 y

⇒ 7 8 y 9 − 4 y 3 8 y 9 + 2 y

⇒ 56 y 9 − 4 y 24 y 9 + 2 y

⇒ 56 y − 36 y 9 24 y + 18 y 9

⇒ 20 y 9 42 y 9

⇒ 20 y 9 × 9 42 y ⇒ 1021

Thus, the ratio found is

10 : 21

.
Therefore, option 3 is correct.

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