Question

If the numbers in each of the following groups are in proportion, what is the value of the variable in each group?

(1) 6, x, 10, 15
(2) p, 9, 8, 6
(3) 25, 35, 35, m

Answer 1

(1) For the set of numbers 6, x, 10, 15:
The given numbers in the set are in proportion. So, the ratios 6 : x and 10 : 15 must be equal.

$$\begin{gathered} \Rightarrow \frac{6}{x}=\frac{10}{15} \\ \Rightarrow x=9 \end{gathered}$$

∴ Value of x should be 9.

(2) For the set of numbers p, 9, 8, 6:
The given numbers in the set are in proportion. So, the ratios p : 9 and 8 : 6 must be equal.
$$\begin{gathered} \Rightarrow \frac{p}{9}=\frac{8}{6} \\ \Rightarrow p=12 \end{gathered}$$

∴ Value of p should be 12.

(3) For the set of numbers 25, 35, 35, m:
The given numbers in the set are in proportion. So, the ratios 25 : 35 and 35 : m must be equal.

$$\begin{gathered} \Rightarrow \frac{25}{35}=\frac{35}{m} \\ \Rightarrow m=49 \end{gathered}$$

∴ Value of m should be 49.