The followoing compound is named as following: pent -3-ene-1-yne . I wanted to ask why alkyne gets a preference here although alkene is higher in the preference series???

 If the principle chain contains 2 or more multiple bonds, numbering is done in such a way that the multiple bonds get the lowest set of locants.

Therefore, here, pent-3-en-1-yne is preferred over pent-2-en-4-yne

you name the compound is wrong                         but reason is right that you given it is true that alkenes get preference first

          the right name is pent-4-yne-3-ene

From the IUPAC Handbook for Nomenclature of Organic Compounds,

3.3 - Unsaturated unbranched acyclic hydrocarbons having both double and triple bonds are named by replacing the ending "-ane" of the name of the corresponding saturated hydrocarbon with the ending "-enyne", "-adienyne", "-atrienyne", "-enediyne", etcNumbers as low as possible are given to double and triple bonds even though this may at times give "-yne" a lower number than "-ene". When there is a choice in numbering, the double bonds are given the lowest numbers.

Eg : 3-Penten-1-yne

1-Pent-4-yne

I must admit, I'm quite confused by this rule.

Nomenclature mein the first step is finding the longest C-chain (or the one containing max. = n triple bonds)

The second step is finding the nearest locant position......(=/triple bonds r also considered as locants)

Agar chain ke dono end se nearest locant par diff. group hain THEN ONLY u will start assigning the Priority..... or agar same hi groups hain THEN u will go for the Lowest sum rule.....

Without doing one step; u can't jump 2 the next....

So, in the compound....main chain is the st. one with 5-C(s)...... then v have nearest locant @ C-1 frm left as compared to @C-2  frm right....

So, v will start numbering frm the LEFT.... (Priority compare karne ka sawaal hi nahi uthta !!!)

Finally name  -----  Pent-3-en-1-yne