Question

Q3 x and y vary inversely. When 1 point
x = 15, then y = 18. What will be
the value of y when x = 9?
O a) 32
O b) 30
O c) 27
O d) 34​

Answer 1

$\dag\:\:\underline{\sf AnsWer :}$

Here we are given that, x and y vary inversely. Therefore the equation will be :

$:\implies \sf x = \dfrac{k}{y}...(i) \: \: \: \bigg \lgroup \bf{Where \: k \: is \: constant}\bigg \rgroup$

In the question we are also given the value of x = 15 and y = 18. Now just plug in the values of x and y in eqⁿ (i) :

$:\implies\sf 15 = \dfrac{k}{18}$

Transposing the 18 towards LHS we get :

$:\implies\sf 15 \times 18 = k$

$:\implies \underline{ \boxed{\sf k = 270}}$

• Hence, the value of k is 270.

But here we have to find the value of y when x = 9. So, put the known values in eqⁿ (i)

• x = 9
• k = 270

$\dashrightarrow\:\:\sf 9 = \dfrac{270}{y}$

$\dashrightarrow\:\:\sf y= \dfrac{270}{9}$

$\dashrightarrow\:\: \underline{ \boxed{\sf y= 30}}$

Hence, Option (b) 30 is the correct answer.

Answer 2

Given:

• x = 15,then y = 18.

To Find:-

• What will be the value of y when x = 9?

Solution:-

Here, given that x and y vary inversely. The equation will be :

$\sf \implies \: x = \frac{k}{y} .(i) \:$

(where K is constant)

The value given in question x = 15 and y = 18.Put the value in the equation (i):

$\sf \implies15 = \frac{k}{18} \\ \\ \sf \implies15 \times 18 = k \\ \\ \sf \implies \: k = 270$

Hnece,the value of K is 270.

The value of x = 9 given here and we have to find the value of y but the value in equation (i)

$\sf \implies \: x = 3 \\ \\ \sf \implies \: k = 270 \\ \\ \sf \implies \: 9 = \frac{270}{3} \\ \\ \sf \implies \: y = 30$