Question

Y varies directly with X and has a constant rate of change of 6. When the value of Y is 11, then the value of X could be _____.

Answer 1

Answer:  The correct option is (B) less than 2.

Step-by-step explanation:  Given that Y varies directly with X and has a constant rate of change of 6.

We are to find the possible value of X when the value of Y is 11.

Since Y varies directly with X, so we can write

$Y\propto X\\\\\Rightarrow Y=kx~~~~~~~~~~~~~~~(i),~~~~~~~~~\textup{[where 'k' is the constant of variation]}$

Since the rate of change is constant and is equal to 6, so we must have

$k=6.$

So, from equation (i), we have

$Y=kX\\\\\Rightarrow Y=6X~~~~~~~~~~~~~~~~~~~~~~(ii)$

Now, when Y = 11, then from equation (ii), we get

$Y=6X\\\\\Rightarrow 11=6X\\\\\Rightarrow X=\dfrac{11}{6}$

Thus, the value of X is less than 2 when Y = 11.

Option (B) is CORRECT.