Choose the correct synonyms of the underlined word.
Immigrants have always been prepared to work hard and in appalling conditions for the sake of their descendants.

• We have to seek out the meaning of sake and also the meaning of words that are given within the options. And both words should have an identical meaning or a precise sense.
• The meaning of sake is for the aim of. And that we should find the proper answer from the choices given whose meaning is that the same as of sake.
• Option A) Benefit - is the correct answer because the meaning of benefit is ‘getting advantage or benefit from something, and this is often the synonym of sake because they both have identical meanings. Thus, this can be the right answer.
• Option B) Health - is an incorrect answer because the meaning of health is ‘being free from illness or injury, and this is often not a synonym for sake. Thus, this is often an incorrect answer because the meaning of the words ‘health’ and ‘sake’ doesn't match.
• Option C) Property - is an incorrect answer because the meaning of property is ‘thing or things belonging to someone, and this is often not a synonym of sake. Thus, this is often an incorrect answer because the meaning of the words ‘property’ and ‘sake’ doesn't match.
• Option D) Entertainment - is an incorrect answer because the meaning of entertainment is ‘amusement or enjoyment, and this is often not a synonym for sake. Thus, this can be an incorrect answer because the meaning of the words ‘entertainment’ and ‘sake’ doesn't match.

Hence, option A is the correct answer.