question_answer

Observe the following table, where x and y are in inverse variation:

X	(i) \[{{p}_{1}}\]	200	300
y	60	30	(ii) \[{{p}_{2}}\]

Find the unknown quantities.

Answer:

Let                       \[{{x}_{1}}={{p}_{1}},{{x}_{2}}=200,{{x}_{3}}=300\]

and                       \[{{y}_{1}}=60,{{y}_{2}}=30,{{y}_{3}}={{p}_{2}}\]

Since, x and y are in inverse variation.

(a) \[\therefore \]             \[{{x}_{1}}{{y}_{1}}={{x}_{2}}{{y}_{2}}\]

\[\Rightarrow \]               \[{{p}_{1}}\times 60=200\times 30\]

\[\therefore \]                  \[{{p}_{1}}=\frac{200\times 30}{60}=100\]

(b) Also,                \[{{x}_{2}}{{y}_{2}}={{x}_{3}}{{y}_{3}}\]

\[\Rightarrow \]                       \[200\times 30=300\times {{p}_{2}}\]

\[\therefore \]      \[{{p}_{2}}=\frac{200\times 30}{300}=20\]