you are not paying attention to the pressure or the number of moles in the solution, so you do not need the R constant either, so generally what you do know is the volume and the temperature.

~~P~~V=~~n~~~~R~~T

V_{1}=T_{1}

-what this says is that you are observing the volume and temperature through the entire experiment, so you also need to have an equation for the end.

V_{2}=T_{2}

we try to set a value that is equation on both equation such as,

V_{1}/T_{1}=1 -and- 1=V_{2}/T_{2}

to get that you only needed to divide T and T divided by itself is 1, but now we have that both equations are equal to one and we could say that:

V_{1}/T_{1}=V_{2}/T_{2}

which is the same as choice (a), but that is how the equation is set up before solving a problem, just explained step by step, does not really need all these calculations you are simply supposed to learn them subconciously, now to say what would the answer be b and not c or d well we are trying to solve for an unknown value. lets say that they give you the volume for the beginning and the temperature, if they give the volume or the temperature when the solution goes to completion you could arrange the problem algebraically so that you could solve for the equation, just set it equal to the value that you are not given and then substitute.

by multiplying both sides by the denominator of each side of the equation you get that

V_{1}V_{2}=T_{1}T_{2}

well you can say that it cannot be

V_{1}V_{1}=T_{2}T_{2}

and there is your answer explained specifically :Lighten: