Question: Say I have one old and one new bike.

Should I write:

> 
> Both the old and the new bike should be there.
> 
> 
> 

or

> 
> Both the old and the new bike**s** should be there.
> 
> 
>

Answer: 
The first is more specific: you have one of each.

The second is less specific: you have a mixture of old and new bikes.
> 
> **Both the old bike and the new bike should be there**.
> 
> 
> 

**The old bike** is singular

**The new book is singular**

So the old bike and the new bike are plural and mean one old book and one new book.

So the above sentence is correct.

If you say :

> 
> **Both the old and the new bikes**, it means some old bikes and some new bikes.
> 
> 
> 

It is not what you intended to say