Question

6. x and y vary directly. When x = 3, then y
= 36. What is the value of x when y =
96?
(a) 4
(b) 6
(c) 8
(d) 12
​

Answer 1

Answer:

X=8

Step-by-step explanation:

It can be written as

3/36=x/96

x=3×96/36

=8

Answer 2

The value of x = 8

Given :

x and y vary directly

When x = 3, then y = 36

To find :

The value of x when y = 96

(a) 4

(b) 6

(c) 8

(d) 12

Solution :

Step 1 of 2 :

Find value of constant of variation

Here it is given that x and y vary directly

$\sf x \propto y$

∴ x = ky - - - - - - (1)

Where k is constant of variation

Now y = 36 when x = 3

Thus we get

3 = 36k

⇒ k = 3/36

⇒ k = 1/12

From Equation 1 we get

$\displaystyle \sf{x = \frac{1}{12}y } \: \: \: - - - - (2)$

Step 2 of 2 :

Find the value of x

Now it is given that y = 96

From Equation 2 we get

$\displaystyle \sf{x = \frac{1}{12} \times 96 }$

$\displaystyle \sf{ \implies x = 8}$

So the required value of x = 8

Hence the correct option is (c) 8

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