Hint:Luxury is a word which is used to describe something that helps in adding to pleasure or comfort and make life easier.
Complete step-by-step answer:
Luxury basically means to have excess of anything or extravagance.
Option A sadness is an incorrect option and it is a word which is used for showing sorrow and it is an opposite for Happiness so it cannot be an opposite for Luxury. Sadness is an emotion of a personality.
Option B is Treachery is an incorrect option because the meaning of the word Treachery is disloyalty or betrayal. For example, the maid was found to treachery towards the owner. Option C is Duplicity is an incorrect option as the meaning of the word is deceit or dishonesty that means it can be an opposite for honesty but cannot be an opposite of luxury.
Option D is Austerity is a correct option means simplicity. Hence, the opposite of the word Luxury is Austerity. Which means the correct and appropriate answer for this question is D. Austerity which has the meaning of simplicity. For example, the children living near the hill area live their life with austerity.
Option D is the correct answer.
Note:Luxury can also be used to describe something which has a high price range and usually adopted by high class people. Luxury can include luxurious cars, homes, and even food. For example: The royal highness cannot travel in a car without a luxurious interior. OR She cannot adjust because she used to sleep on a luxurious bed in her house.