Question

Complite the following table given that x varies directly as y .

x	5	...	10	35	25	...
y	8	12	...	...	...	32

Answer 1

\[\text{ Here, x and y vary directly }  . \]
\[ \therefore x = ky\]

\[ x = 5 \text{ and } y = 8\]
\[i . e . , 5 = k \times 8\]
\[ \Rightarrow k = \frac{5}{8} = 0 . 625\]
\[\text { For y = 12 and k = 0 . 625, we have } : \]
\[x = ky\]
\[ \Rightarrow x = 12 \times 0 . 625 = 7 . 5\]
\[\text{ For x = 10 and k = 0 . 625, we have: } \]
\[x = ky\]
\[ \Rightarrow 10 = 0 . 625 \times y\]
\[ \Rightarrow y = \frac{10}{0 . 625} = 16\]
\[\text{ For x = 35 and k = 0 . 625, we have: } \]
\[x = ky\]
\[ \Rightarrow 35 = 0 . 625 \times y\]
\[ \Rightarrow y = \frac{35}{0 . 625} = 56\]
\[\text{ For x = 25 and k = 0 . 625, we have: } \]
\[x = ky\]
\[ \Rightarrow 25 = 0 . 625 \times y\]
\[ \Rightarrow y = \frac{25}{0 . 625} = 40\]
\[\text{ For y = 32 and k = 0 . 625, we have } : \]
\[x = ky\]
\[ \Rightarrow x = 0 . 625 \times 32 = 20\]