For example, I am preparing a report for 1-10 of the month, then 11 to 20 and then 21 to 30. Is there any specific word for 10 days in English like weekly report which consist of 7 days?
As others suggested, there is no English word that could mean "10 days". But the term "10 day" is broadly used for weather forecast and report. You can use
- 10-day report for the first 10 days of a month
- 10-day report for the middle 10 days of a month
- 10-day report for the last 10 days of a month
Based on context, you can use the first/middle/last part of a month.
Example: MANDATED 10-DAY REPORT
[Maryland Board of Physicians]
The reason there is no satisfactory term is that we traditionally use a week which is inconsistent with the decade. Most people used non-metric units for most things before the French Revolution. The revolutionaries tried to metricate everything. Some were popular, like the metre, and some weren't, like the 10-day week and the 10-month year.
A decad (note: not decade) is:
A group or set of ten.
Although not specific to days, if you divide a calendar month¹ in a set of three decads, it should be clear from context that it will refer to sets of ten days. For example:
For a higher resolution analysis, we divide each month in three decads, as shown in Figure 12, which shows...
The meaning in this context should be clear even to readers who are not familiar with the term decad. And who knows, you might set a trend ;-)
I have seen this usage in a context of climate and weather data analysis.
¹In climate models, a year consists of twelve months of exactly 30 days each. In this case, the division in three decads is exact.
10 days in a metric week (called a dekade).