If a : b : c = 3 : 2 : 4 and b : d = 2 : 3, then find the value of $\left(\frac{a+c+d}{c-d}\right)^3$.
Answer & explanation
Correct answer: option 3
a : b : c = 3 : 2 : 4
b : d = 2 : 3
= $\left(\frac{a+c+d}{c-d}\right)^3$
= $\left(\frac{3x+4x+3x}{4x-3x}\right)^3$.
= $\left(\frac{10x}{1x}\right)^3$
= \( {10 }^{3 } \) = 1000.