Name: Direct Proportion
Uploaded: 2019-07-19
Duration: 2 min 15 s
Description: Watch this session to learn about direct proportion in detail with examples....

Question

Observe the following tables and find if $x$ and $y$ are directly proportional:

$x$	$20$	$17$	$14$	$11$	$8$	$5$	$2$
$y$	$40$	$34$	$28$	$22$	$16$	$10$	$4$

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.

$x$ $20$ $17$ $14$ $11$ $8$ $5$ $2$

$y$ $40$ $34$ $28$ $22$ $16$ $10$ $4$

Two variables $x & y$ are said to be in direct variation if the ratio between $x & y$ is a constant, i.e. $\frac{x}{y} = k$ .

So let us find the constant ratio in each case.

When $x = 20, y = 40$ then constant ratio is $\frac{x}{y} = \frac{20}{40} = \frac{1}{2}$

When $x = 17, y = 34$ then constant ratio is $\frac{x}{y} = \frac{17}{34} = \frac{1}{2}$

When $x = 14, y = 28$ then constant ratio is $\frac{x}{y} = \frac{14}{28} = \frac{1}{2}$

When $x = 11, y = 22$ then constant ratio is $\frac{x}{y} = \frac{11}{22} = \frac{1}{2}$

When $x = 8, y = 16$ then constant ratio is $\frac{x}{y} = \frac{8}{16} = \frac{1}{2}$

When $x = 5, y = 10$ then constant ratio is $\frac{x}{y} = \frac{5}{10} = \frac{1}{2}$

When $x = 2, y = 4$ then constant ratio is $\frac{x}{y} = \frac{2}{4} = \frac{1}{2}$

Here, the constant ratio is same for all values of $x$ and $y$ .

Hence, we can state that $x$ and $y$ are in direct variation.

$x$	$5$	$8$	$12$	$15$	$18$	$20$
$y$	$15$	$24$	$36$	$60$	$72$	$100$

Time period	$1$ year	$2$ years	$3$ years
Simple Interest (in $₹$ )
Compound Interest (in $₹$ )

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