Пусть бритва и новая, брат всё равно предпочитает бриться вечером, а не утром.

Although the razor is new, my brother still prefers to shave in the evening and not in the morning.

Breakdown of Пусть бритва и новая, брат всё равно предпочитает бриться вечером, а не утром.

• новый: new
• брат: the brother
• вечером: in the evening
• утром: in the morning

Questions & Answers about Пусть бритва и новая, брат всё равно предпочитает бриться вечером, а не утром.

What does пусть mean here? Is it the same пусть as in Пусть он войдёт?

Not exactly. In Пусть он войдёт, пусть means let: Let him come in.

In your sentence, пусть is being used in a concessive sense, meaning something like:

• although
• even if
• granted that

So Пусть бритва и новая... means Even though the razor is new... or Granted, the razor is new...

This use is fairly common in Russian and often sets up a contrast with the main clause.

Why is there an и in Пусть бритва и новая?

This и is part of the concessive pattern. In sentences like this, пусть ... и ... often has the sense of:

• even though ... is ...
• granted that ... is ...

So:

• Пусть бритва и новая = Even though the razor is new

The и does not simply mean and here in the normal additive sense. It helps reinforce the idea of concession.

A rough structural parallel would be:

• Пусть он и устал, он продолжает работать.
• Even though he is tired, he keeps working.