V+ 었더니/았더니/였더니

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 조금 후에 요금소가 나오는데 제 가방에 있는 지갑 좀 주세요.

In a little while there will be a toll gate, so take out my wallet from my bag, please.
아니에요. 운전하느라고 고생하시는데 제가 낼게요.
No. You are going through the trouble of driving so I will pay.
그런데 왜 저 차들은 파란색 도로로 가요?
But why are those cars going on the blue-colored road?
하이패스 단말기를 단 차들이에요. 제 차에도 달았더니 후불로 결제해서 편하더라고요.
Those are cars that have a Hi-Pass card reader installed. I have it installed on my card so I pay in installments and it's very convenient.
미리 돈을 준비할 필요가 없으니 편하겠어요.
There is no need to prepare money in advance so, it is convenient.
게다가 여러가지 할인 혜택도 있어서 좋아요.
Besides, it is good that there are also various discounts.

V+ 었더니/았더니/였더니
As it is attached to an action verb's stem, it is used when the speaker's behavior is completed or his experience can be the cause or effect.

'-았더니' is used if the ending syllables of an action verb's stem are 'ㅏ, ㅗ'. Other than that, '-었더니' is used if it ends with a vowel (ㅓ, ㅜ, ㅡ,ㅣ). '-였더니(했더니)' is used when '하-' is used.

방학동안 열심히 운동을 했더니 살이 많이 빠졌어요.
After I exercised a lot over vacation, I lost a lot of weight.

서비스 센터에서 수리를 받았더니 컴퓨터 속도가 아주 빨라졌어요.
After I got a repair from the service center, the speed of my computer became very fast.

따뜻한 우유를 마시고 잤더니 숙면을 취할 수 있었어요.
After I drank warm milk, I was able to sleep deeply.

Related words
요금소 tollgate
도로 road
하이패스 high-pass
High-pass is a system that allows tolls on highways to be paid using infrared or frequency. The terminal that inserts the electronic card is installed in the car and the toll is automatically paid after passing the toll gate.
단말기 card reader
(기기를) 달다 (machine) to install
후불 deferred payment
게다가 in addition
혜택 discount
숙면을 취하다 to sleep deeply

Source: Yonsei University. Korean Language Institute

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