kare ha kekka wo sugu siritagaru node, siken ga owaru tabi ni sensei ni kikimasu.

Because the sentence is talking about someone else’s desire: he wants to know.

In Japanese, ～たい is most naturally used for the speaker’s own desire, or sometimes in questions about the listener’s desire. For a third person, Japanese usually uses ～たがる to describe an observable desire.

So:

• 知りたい = want to know
• 知りたがる = show signs of wanting to know / seem to want to know

Here, 彼は結果をすぐ知りたがる means that he tends to want to know the results right away.

It is made from the verb 知る:

• dictionary form: 知る = to know
• verb stem: 知り
• add たがる
• result: 知りたがる

So:

• 知る → 知りたがる

This pattern is common:

• 食べたい → 食べたがる
• 行きたい → 行きたがる
• 見たい → 見たがる

Also, たがる behaves like a regular verb after that:

• 知りたがります = polite
• 知りたがった = past
• 知りたがっている = is showing signs of wanting to know

Because they are doing different jobs in the sentence.

• 彼は marks the main topic of the whole sentence: as for him...
• 試験が is the subject inside the smaller clause 試験が終わる = the exam ends

So the structure is roughly:

• 彼は ... 聞きます
  As for him, he asks...
• 試験が終わるたびに
  every time an exam ends

A very common pattern in Japanese is:

• main sentence topic marked by は
• subject inside a subordinate clause marked by が

Because 結果 is the direct object of 知る.

• 結果を知る = to know the result
• 結果をすぐ知りたがる = to want to know the result right away

So を marks the thing he wants to know.

Because Japanese usually uses the plain form before grammar like ので and たびに.

Here:

• 知りたがるので = because he wants to know
• 終わるたびに = every time it ends

The final verb of the main sentence is where the politeness is shown:

• 聞きます = polite

So this is completely normal. It is not a mistake or mismatch.

A rough pattern is:

• subordinate parts: plain form
• final main verb: polite form if the sentence is polite

ので means because or since.

So:

• 結果をすぐ知りたがるので、先生に聞きます
• Because he wants to know the results right away, he asks the teacher.

Compared with から, ので often sounds a bit softer, more explanatory, or more neutral.

So:

• ～から = because, often a bit more direct
• ～ので = because, often a bit gentler or more explanatory

Both can often be translated as because in English.

たびに means every time or whenever.

It follows a verb in dictionary form:

• 終わるたびに = every time it ends
• 試験が終わるたびに = every time an exam ends

So the whole phrase means:

• whenever a test/exam is over
• every time an exam ends

This shows a repeated action, not just one single event.

Because the expression is fixed as たびに.

You should learn it as one grammar pattern:

• Verb dictionary form + たびに
• Noun + の + たびに

Examples:

• 行くたびに = every time I go
• 会うたびに = every time I meet
• 試験のたびに = every exam / every time there is an exam

In your sentence, it uses the verb version:

• 試験が終わるたびに

Because 聞く can mark the person being asked with に.

So:

• 先生に聞く = ask the teacher

Here, 先生 is the person he asks.

This is a very common pattern:

• 友達に聞く = ask a friend
• 店員に聞く = ask the store clerk
• 先生に聞く = ask the teacher

In Japanese, the non-past form can express:

• present
• future
• habitual/repeated action

Here, because of たびに = every time, the meaning is habitual:

• he asks the teacher every time an exam ends

So 聞きます here is best understood as a repeated habit or regular action, not one single future event.

すぐ most directly modifies 知りたがる.

So the idea is:

• he wants to know the results right away

That desire is the reason he asks the teacher.

So the flow is:

• he wants to know immediately
• therefore he asks the teacher after each exam

In English, right away might feel like it could apply to the asking too, but in the Japanese sentence it is placed before 知りたがる, so it most naturally goes with wanting to know.

Japanese often uses a noun without marking singular/plural the way English does.

So 試験 can mean:

• an exam
• exams
• the exam, depending on context

Because the sentence has たびに = every time, the meaning naturally becomes repetitive:

• every time an exam ends
• after each exam

So even though 試験 looks singular in English terms, the sentence clearly implies repeated exams from the context.