Earlier I used to stay separate with my wife and kids but now since some time my mother has come to stay in my house due to some health reasons . Now i do not have any separate room thus this affects my privacy with my wife . I have a wajib duty to take care of my mother but also there is a body need too which needs to fulfil. I stay disturbed and cannot concentrate on my work and ibadat because of not having physical relationship with my wife . In this situation is it permissible to masturbate to relieve this problem .

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No you cannot, it's better to find some time while kids not in room or when they are sleeping or you can arrange somewhere else.