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If x: y = 3: 5, then what is the value of the ratio $3 x + 4 y : 8 x + 5 y$ ?

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1 : 2

3 : 1

29 : 49

1 : 4

answer is C.

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Detailed Solution

Given,
x: y = 3: 5
Let

x = 3 a

and

y = 5 a .

The ratio of given fraction is,

⇒ 3 x + 4 y : 8 x + 5 y ⇒ 3 × 3 a + 4 × 5 a : 8 × 3 a + 5 × 5 a

⇒ 9 a + 20 a : 24 a + 25 a

⇒ 29 a : 49 a

⇒ 29 : 49

Thus, if

x : y = 3 : 5

, then the ratio of

3 x + 4 y : 8 x + 5 y

is 29: 49.
Thus, option 3 is correct.

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