Question

In the following table, check whether $x$ and $y$ are in direct variation. Find the value of the constant ratio also.

$x$	$7$	$9$	$13$	$21$	$25$	$30$	$41$
$y$	$21$	$27$	$39$	$63$	$75$	$90$	$123$

Accepted Answer

From the given table, we have to check whether $x$ and $y$ are in direct variation. If they are then we have to find the value of the constant ratio.

$x$ $7$ $9$ $13$ $21$ $25$ $30$ $41$

$y$ $21$ $27$ $39$ $63$ $75$ $90$ $123$

Two variables $x & y$ are said to be in direct variation if the ratio between $x & y$ is a constant, i.e. $\frac{x}{y} = k$ . We need to find the value of constant ratio $k$ for each pair of $x & y$ . So lets find the constant ratio in each case.

When $x = 7, y = 21$ then constant ratio is $\frac{x}{y} = \frac{7}{21} = \frac{1}{3}$

When $x = 9, y = 27$ then constant ratio is $\frac{x}{y} = \frac{9}{27} = \frac{1}{3}$

When $x = 13, y = 39$ then constant ratio is $\frac{x}{y} = \frac{13}{39} = \frac{1}{3}$

When $x = 21, y = 63$ then constant ratio is $\frac{x}{y} = \frac{21}{63} = \frac{1}{3}$

When $x = 25, y = 75$ then constant ratio is $\frac{x}{y} = \frac{25}{75} = \frac{1}{3}$

When $x = 30, y = 90$ then constant ratio is $\frac{x}{y} = \frac{30}{90} = \frac{1}{3}$

When $x = 41, y = 123$ then constant ratio is $\frac{x}{y} = \frac{41}{123} = \frac{1}{3}$

Hence, we can state that $x$ and $y$ are in direct variation and the constant ratio is $\frac{1}{3}$ .

$x$	$2.5$	$7.5$	$\frac{x}{y} = \frac{30}{90} = \frac{1}{3}$	$17.5$	$19$
$y$	$x = 41, y = 123$	$7.5$	$11$	$17.5$	$19$

$x$	$5$	$6$	$7$	$8$	$9$	$11$
$y$	$25$	$24$	$35$	$40$	$50$	$66$

$x$	$1$	$2$	$3$	$4$	$5$
$y$	$2$	$1$	$\frac{2}{3}$	$\frac{1}{2}$	$\frac{2}{5}$

Chhattisgarh Board Solutions for Chapter: Direct and Inverse Variation, Exercise 3: EXERCISE 7.1

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Chapter: Direct and Inverse Variation, Exercise 3: EXERCISE 7.1

Questions from Chhattisgarh Board Solutions for Chapter: Direct and Inverse Variation, Exercise 3: EXERCISE 7.1 with Hints & Solutions

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