Question

Fill in the blanks in each of the following so as to make the statement true:
(i) Two quantities are said to vary.... with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same.
(ii) x and y are said to vary directly with each other if for some positive number k,...... = k.
(iii) If u = 3 v, then u and v vary .... with each other.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{directly} \\ \left(\mathrm{ii}\right)xa\mathrm{nd}ya\mathrm{re}\mathrm{said}\mathrm{to}\mathrm{vary}\mathrm{directly}\mathrm{with}\mathrm{each}\mathrm{other}\mathrm{if}\frac{x}{y}=k,\mathrm{where}k\mathrm{is}\mathrm{a}\mathrm{positive}\mathrm{number} \\ \left(\mathrm{iii}\right)\mathrm{because}u=3v,u\mathrm{and}y\mathrm{vary}\mathrm{directly}\mathrm{with}\mathrm{each}\mathrm{other} \end{gathered}$$