nation holiday 15-aug falls in continue absent

Yes of course. He is eligible for it.

Dear All
In Tiruchengode Mills Workers Union v Industial Tribunal, Madras (1964 (2) LLJ 404), Madras High Court has held that the right of the workmen for holiday with wages is subject to the right of the employer given under sub-sec (2) of Sec 5, to call upon the workmen to come and work on such Holidays. Therefore in case of continuous absence, leave or strike, employer need not give holiday with wages.Regards.
N Nataraajhan, Sakthi Management Servies (Hp : + 91 94835 17402 ; E-mail : [Login to view])

Leave Rules are basically for minimum leave to be given, categories of leave like CL PL SL. During Privilege Leave (Earn Leave) National Holidays are excluded. As far as National Holiday is concerned I do not find any reason of marking CL SL leave on National Holiday and also do not find any exemption for the same if any employee remain on leave before and after such Holiday.
You may include the same in your Standing order if you want so.
Regards
RB

Dear Mahesh
I think this has not happened for the first time in your organisation, follow the leave rule of your organisation. You need to determine the category of your organisation and follow relevant rules of the state where it exist, if no set leave rule is there.
One need to understand what is a paid holiday. If a person works on any paid holiday is paid ordinarily double the rate of wages or a leave in lieu of wages or as per the rule of that state.
There are several set rules framed under diffrent acts on interpretation of leave & holidays i.e. National & Festival Holidays Act-1963, Factory Act-1948, Shops & Commercial Establishment Act and The Industrial Employment (Standing Orders) Act, 1946, etc. There are organisations do not consider 'Paid Holiday' in leave for example on three days of leave, the leave is considered as two days.

Dear Mahesh,
In our organisation if we take upto 3 leaves it will considered as CL and more than 3 leaves it considered as PL. If employee is availing CL then it will not count in any Sunday / holiday in between leaves but if employee is availing PL then it will use sandwich leaves, i mean all the Sunday/ holiday falls in between leaves will be count. so as per your query August 15 shall not be considered as leave as he has taken leave one day prior i.e. on August 14 and one day after i.e. on August 16.