1

その手紙を送るのに100円かかった。

その手紙の送るのに100円かかった。

その手紙の送りは100円かかった。

4

1) その手紙{てがみ}送{おく}るのに100円{えん}かかった。

2) その手紙送るのに100円かかった。

3) その手紙の送りは100円かかった。

Among the three sentences, only the first one is correct, grammatical and natural-sounding. It is just perfect.

Sentence #2 is incorrect for using the first 「の」 as 「手紙」 is the direct object for the verb 「送る」. We must use 「を」 instead.

Sentence #3 is also incorrect for using 「送り」. We simply do not say 「その手紙の送り」. If you replaced 「送り」 by 「送料{そうりょう}」("postage"), the sentence would be acceptable.

2

The correct sentence is the first one. The rest are wrong.

送り is a tricky masu-stem-derived noun which appears only in several set phrases such as コマ送り, 早送り and 送り仮名.

If you want a noun-based expression, you can use 送料 and say:

  • その手紙の送料は100円だった。
  • その手紙の送料として100円かかった。
0

The first sentence is correct.

The second is incorrect for using a verb following the case particle 「の」. If you want to use it, it'll be OK to say 「その手紙の送ることのために」。

The third is incorrect because the word 「送り」is rarely used alone.

  • 1
    「その手紙の送ることために」: の is missing after こと, although "送ることのために100円かかった" would sound like you did not want to pay 100 yen. – naruto Feb 7 '18 at 8:36
  • 1
    その手紙を送るために is okay, but その手紙を送ることのために is unnaturally wordy and I would feel there were some reason to emphasize this part. Maybe it might look more or less closer to "It took me 100 yen TO SEND THE LETTER." – naruto Feb 7 '18 at 9:17
  • I'm sorry to have pressed the enter. I didn't know I have already sent it... – Surreal Feb 7 '18 at 9:23
  • Correct. The reason why I added こと is the の. And I think 「のに」and 「ために」 are both objective. The mood only depends on the content afterwards, if any. – Surreal Feb 7 '18 at 9:31

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