Question

m α n, n = 15 when m = 25. Hence
(1) Find m when n = 87
(2) Find n when m = 155

Answer 1

Since, m α n

$\Rightarrow m=kn$, where k is proportional constant.

We have, n = 15 when m = 25.

$$\begin{gathered} \Rightarrow 25=k\times 15 \\ \Rightarrow k=\frac{25}{15} \\ \Rightarrow k=\frac{5}{3} \end{gathered}$$
So, $m=\frac{5}{3}n$ ...(i)

(1) We have, n = 87

By using equation (i), we get

$m=\frac{5}{3}\times 87=5\times 29=145$

(2) We have, m = 155

By using equation (i), we get

$$\begin{gathered} 155=\frac{5}{3}n \\ \Rightarrow n=\frac{3}{5}\times 155=3\times 31=93 \end{gathered}$$