Day Questions

If one performs tayammum instead of ghusl of janabah, how long will its taharah last? Is its affect the same as that for the ghusl, so it lasts until the next time one sustains a major occurrence (hadath akbar) like janabah, menstruation or touching a dead body?

The tayammum becomes invalid with the elimination of the justification that caused one to perform tayammum. For example, if the patient who performed the tayammum instead of ghusl due to his illness was cured, then the tayammum is invalid immediately and ghusl will be required. The tayammum also becomes invalid also if the justification continued but the individual sustained another major occurrence (hadath akbar).

Regarding khums, suppose I purchase a box of 100 pens from a store. But I only use 20 of those pens in one year. Is there khums due on the remaining 80 pens? Or are they all considered to be "used" as soon as I open the original box from the store? I have a similar question about a notebook. Suppose I buy a notebook with 100 pages and only use 20 of those pages. Is there khums due on the unused paper in that notebook (80 pages) after one year from its purchase? Or is khums no longer due the moment I wrote in one page of the notebook?

If what you need can only be obtained in a larger quantity, then khums is not applicable on what remains from that. For example, if you need a notebook of 20 pages, but you could not find a 20-page notebook, and the closest to it is a 100-page notebook, then the unused part of the notebook will not be subject to khums. Similarly, if you need 20 pens, and you can purchase 20 pens without needing to buy 100 pens, then the unused pens will be subject to khums.

Does washing clothes with detergent in a washing machine make the najis clothes tahir?

If one piece of clothing is najis, then washing it with tahir clothes makes all clothes being washed najis even if detergent is used. They do not become tahir again unless they were washed with unmixed tahir water.