Can I install Ubuntu on a logical partition ? What will be the advantage or disadvantage of using a logical partition to install Ubuntu 12.04?

There is no advantage or disadvantage of installing Ubuntu on a primary or logical partition. The only "drawback" if you can call it that way is that if you select logical, the names of the /dev/sd will start at 5. But if you select primary they will start at 1.

For example:

Primary

/dev/sda1
/dev/sda2
...

Logical

/dev/sda5
/dev/sda6
...

Basically is nothing to worry about.

As far as I can see, you are good to go installing Ubuntu on that 55GB space you have left in your logical space. The one I mean is this:

So no need to worry about it. Just install it and enjoy.

Logical partitions exist to overcome the limitation of MBR (Master Boot Record) which only permits 4 "physical" (IE non logical) partitions. There is no difference in operation between logical and physical partitions.

It's arguably better to use logical partitions as it allows the creation of more than 4 partitions in the future. 1 logical partition group takes up one physical partition space but can hold lots (don't know the limit) of logical partitions.

You can install Ubuntu on any partition. In fact, I never create primary partitions at all; I create one big extended partition, and all installations are installed in this extended partition (I don't have Windows, though).

Using this method, you are not limited to 4 partitions, and it's much easier to resize partitions if needed. I don't know of any downside to not using primary partitions at all.