Question

x and y are in direct proportion , when x is 8 and y is 12 . Which of the following is not a possible pair of corresponding values of x and y?

Answer 1

Answer:

It is 6 and 9

Step-by-step explanation:

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Answer 2

15 and 20 is not a possible pair of corresponding values of x and y

Correct question : x and y are in direct proportion, when x is 8, y is 12. Which of the following is not a possible pair of corresponding values of x and y? (a) 10 and 15 (b) 2 and 3 (c) 6 and 9 (d) 15 and 20

Given :

x and y are in direct proportion, when x is 8, y is 12

To find :

Which of the following is not a possible pair of corresponding values of x and y

(a) 10 and 15

(b) 2 and 3

(c) 6 and 9

(d) 15 and 20

Solution :

Step 1 of 2 :

Find value of constant of variation

Here it is given that x and y are in direct proportion

$\sf x \propto y$

$\displaystyle \sf{ \implies y \propto \: x}$

∴ y = kx - - - - - - (1)

Where k is constant of variation

Now y = 12 when x = 8

Thus we get

12 = 8k

⇒ k = 12/8

⇒ k = 1.5

From Equation 1 we get

$\displaystyle \sf{y = 1.5x } \: \: \: - - - - (2)$

Step 2 of 2 :

Choose the correct option

Check for option (a)

Putting x = 10 , y = 15 in Equation 2 we get

15 = 1.5 × 10

⇒ 15 = 15

So x = 10 , y = 15 is a possible pair

Hence this option is not correct

Check for option (b)

Putting x = 2 , y = 3 in Equation 2 we get

3 = 1.5 × 2

⇒ 3 = 3

So x = 2 , y = 3 is a possible pair

Hence this option is not correct

Check for option (c)

Putting x = 6 , y = 9 in Equation 2 we get

9 = 1.5 × 6

⇒ 9 = 9

So x = 6 , y = 9 is a possible pair

Hence this option is not correct

Check for option (d)

Putting x = 15 , y = 20 in Equation 2 we get

20 = 1.5 × 15

⇒ 20 = 22.5

So x = 15 , y = 20 is not a possible pair

Hence this option is correct

Final answer : Hence the correct option is (d) 15 and 20

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