Hi Meghanjalli.. :)
Its just asking if all input prices doubles then what happens.
Its obvious that the cost will get doubled.
Its because: How do we find a cost function?
We minimize "wl+rk" subject to the production function..... (I)
If all input prices will double then, while finding cost we would :
Minimize "2wL+2rk" sub to production function........ (II)
Now, whatever cost you get by minimising (I), you'll get twice of that in (II).
Hence, cost also gets doubled when all input prices doubles.
Note: Main point is "ALL" input prices.
:)