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In the given table, of $x$ and $y$ are inversely proportional, then which of the following are the values of $x 1, y 1$ and $y 2$ ?

x
8
$x_{1}$
16
80
y
$y_{1}$
4
5
$y_{2}$

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x 1 = 10, y 1 = 10 and y 2 = 1

x 1 = 10, y 1 = 10 and y 2 = 15

x 1 = 20, y 1 = 10 and y 2 = 1

x 1 = 10, y 1 = 10 and y 2 = 10

answer is C.

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Detailed Solution

Given,

x	8	$x_{1}$	16	80
y	$y_{1}$	4	5	$y_{2}$

Here, x and y are in inverse proportion.
So, the product remains constant throughout the table, which implies,

x × y = 8 × y 1 = x 1 × 4 = 16 × 5 = 80 × y 2

Calculate the value of

y 1

8 × y 1 = 16 × 5

8 y 1 = 80

⇒ y 1 = 808 ⇒ y 1 = 10

Calculate the value of

x 1

x 1 × 4 = 16 × 5

4 x 1 = 80 ⇒ x 1 = 804 ⇒ x 1 = 20

Calculate the value of

y 2

80 × y 2 = 16 × 5

80 × y 2 = 80 ⇒ y 2 = 8080 ⇒ y 2 = 1

Hence, the required values are

x 1 = 20, y 1 = 10 and y 2 = 1

.
Therefore, option 3 is correct.

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In the given table, of x and y are inversely proportional, then which of the following are the values of x 1 , y 1 and y 2 ? x8x11680yy145y2

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In the given table, of $x$ and $y$ are inversely proportional, then which of the following are the values of $x 1, y 1$ and $y 2$ ?

x
8
$x_{1}$
16
80
y
$y_{1}$
4
5
$y_{2}$