Question

Observe the tables given below and in each case find whether x and y are inversely proportional:
(i)

x	6	10	14	16
y	9	15	21	24

(ii)

x	5	9	15	3	45
y	18	10	6	30	2

(iii)

x	9	3	6	36
y	4	12	9	1

Answer 1

(i)
$$\begin{gathered} \mathrm{Clearly},6\times 9\ne 10\times 15\ne 14\times 21\ne 16\times 24 \\ \mathrm{T}\mathrm{herefore},x\mathrm{and}y\mathrm{are}\mathrm{not}\mathrm{inversely}\mathrm{proportional}. \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{Clearly},5\times 18=9\times 10=15\times 6=3\times 30=45\times 2=90=\left(\mathrm{consant}\right) \\ \mathrm{Therefore},x\mathrm{and}y\mathrm{are}\mathrm{inversely}\mathrm{proportional}. \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{Clearly},9\times 4=3\times 12=36\times 1=36,\mathrm{while}6\times 9=54 \\ \mathrm{i}.\mathrm{e}.,9\times 4=3\times 12=36\times 1\ne 6\times 9 \\ \mathrm{Therefore},x\mathrm{and}y\mathrm{are}\mathrm{not}\mathrm{inversely}\mathrm{proportional}. \end{gathered}$$