If a ∶ b = c ∶ d = e ∶ f = 5 ∶ 7, then what is the ratio (3a + 5c + 11e) ∶ (3b + 5d + 11f)?
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 5 : 7.
a : b = c : d = e : f = 5 : 7
⇒ a : b : c : d : e : f = 5 : 7 : 5 : 7 : 5 : 7
Let, a = 5x, b = 7x, c = 5x, d = 7x, e = 5x, and f = 7x
Now, (3a + 5c + 11e) : (3b + 5d + 11f)
= (3 × 5x + 5 × 5x + 11 × 5x) : (3 × 7x + 5 × 7x + 11 × 7x)
= (15x + 25x + 55x) : (21x + 35x + 77x)
= 95x : 133x
= 5 : 7
Therefore, the required ratio is 5 : 7.