2016 · Q19
If a/b = b/c = c/d, then which of the following is/are correct?1. (b³+c³+d³)/(a³+b³+c³) = d2. (a²+b²+c²)/(b²+c²+d²) = a/d Select the correct answer using the code given below.
Elementary MathematicsRatio and Proportion
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Write a/b = b/c = c/d = 1/t, i.e. a = dt³, b = dt², c = dt. Then (b³+c³+d³)/(a³+b³+c³) = (t⁶+t³+1)/(t⁹+t⁶+t³) = 1/t³ = d/a, whereas (a²+b²+c²)/(b²+c²+d²) = (t⁶+t⁴+1)/(t⁴+t²+1), which is not a/d in general. On the official key the first relation alone is counted correct (the source transcription renders the intended d/a as d), giving 1 only, option A.