Question : What is the ratio of the mean proportional between 1.6 and 3.6 and the third proportional of 5 and 8?
Option 1: 2 : 15
Option 2: 5 : 16
Option 3: 3 : 16
Option 4: 4 : 15
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Correct Answer: 3 : 16
Solution : Mean proportion of 1.6 and 3.6 $=\sqrt{ab}=\sqrt{1.6\times 3.6}=2.4$ Now, the third proportion of 5 and 8 $=\frac{b^2}{a}=\frac{8^2}{5}=\frac{64}{5}$ $\therefore$ Ratio of mean proportion to third proportion = $2.4:\frac{64}{5}$ = 12 : 64 = 3 : 16 Hence, the correct answer is 3 : 16.
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