Chapter 8.2, Problem 12PSB

To determine

To find:The ratio of fourth proportion of two given three terms of the proportion.

Answer to Problem 12PSB

The required ratio is: 4: 5

Explanation of Solution

Given information

The first three terms are 1, 2 and 3

The second three terms are 4, 5 and 6

Formula used

Product of means = product of extremes

Calculation

Let x be the fourth proportion of the terms 1, 2 and 3 and y be the fourth proportion of the terms 4, 5 and 6

Thus we have

  $\begin{array}{l}\frac{1}{2}=\frac{3}{x}\Rightarrow x=6\text{ and}\\ \frac{4}{5}=\frac{6}{y}\Rightarrow y=\frac{6\times 5}{4}=7.5\end{array}$

  $\therefore$ Required ratio

  $\begin{array}{l}=x:y\\ =6:7.5\\ =60:75\\ =4:5\end{array}$