Your HRA computation will be as under:
1. Actual HRA received: 40,000
2. Rent paid over 10% of salary: 50,400 (60000 - 9600)
3. 40% of Salary: 38,400 (40% of 96000) Assuming to be a non-metro city.
Least of above shall be the HRA exemption i.e. Rs. 38,400.
Now accordingly your taxable salary income form 1st company will be as given below:
2,88,000 - 38,400(HRA) - 6500(TA if reimbursed on actual spent amount basis or else only Rs. 6,400) = Rs. 2,43,100
Taxable salary income from 2nd company Rs. 1,40,000
Total Taxable salary for the year: 2,43,100 + 1,40,000 = 3,83,100
Less: Deduction u/s 80C: Rs. 1,00,000
Net taxable income: Rs. 2,83,100
Tax on above Rs. 10,310 [10% of (283100-180000*)]
Add: Education cess of 3% on Rs. 10,310 = Rs. 309
(* 180000 is the basic exemption limit for male.)
Total tax payable = 10310+309=10,619
Less: Tax already deducted Rs. 9,000
Balance tax payable Rs. 1,619 (10,619-9,000)
You will have to pay Rs.1,619 as balance tax before you file your return.
When you say gross salary it means salary including all the allowances and perquisites and when these are deducted from your gross salary it becomes net salary.
You will not get any deduction for the medical expense. Deduction is available only for the medical insurance premium if taken under section 80D upto Rs. 15,000. I think you have not taken any medical insurance policy as such. This deduction is in addition to the limit of Rs.1,00,000 under section 80C, which means if you had paid premium for any medical insurance upto Rs.15,000 you will get a deduction of Rs. 1,15,000 and not just Rs. 1,00,000.
The computation and tax might change if the assumptions that i have taken does not match exactly with you. Like for HRA i have taken a non-metro city, which will change to Rs. 48000 if it is a metro city. In case of TA if it is not on actual reimbursement basis then the limit for TA is only Rs.800 per month so the TA will become Rs. 6400. You should check these before depositing the tax.
Hope the computation is clear to you.