Question : If a : b = 4 : 5 and b : c = 3 : 10, then a : c is:
Option 1: 4 : 10
Option 2: 5 : 3
Option 3: 25 : 6
Option 4: 6 : 25
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Correct Answer: 6 : 25
Solution : a : b = 4 : 5 = 12 : 15 b : c = 3 : 10 = 15 : 50 ⇒ a : b : c = 12 : 15 : 50 ⇒ a : c = 12 : 50 = 6 : 25 Hence, the correct answer is 6 : 25.
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Question : If A : B = 2 : 3 and B : C = 3 : 7, then (A + B) : (B + C) : (C + A) is:
Question : If $a+b+c=5, a^3+b^3+c^3=85$, and $abc=25$, then find the value of $a^2+b^2+c^2-a b- bc - ca$.
Question : If A : B = $\frac{1}{2}:\frac{1}{3}$, B : C = $\frac{1}{5}:\frac{1}{3}$ ,then (A + B) : (B + C) is equal to:
Question : If $a+b+c=6$ and $a^2+b^2+c^2=14$, then what is the value of $(a-b)^2+(b-c)^2+(c-$ a) ${ }^2$?
Question : If $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}$, what is the value of ratio $(C+A)^{2}:(A+B)^{2}:(B+C)^{2}$?
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