By the time or During the time?

Please look at the following question.

"____ the time transportation allowance was common, most of the employees traveled a long distance"
(a)in (b)during (c)at (d)by

The correct answer is (d)by. What I'm curious on is why (b)during can't be the other answer there.

I thought about it.

Now, if the questioner asked me like this,

"_____ the time transportation allowance was common,most of the employees had traveled a long distance".

Can I select (b)during as a right answer?

Thank you for your answer in advance.