Dear Pon, your statement is incorrect. More correctly, it needs a rider to ensure juniors do not make a mistake.
1. The Income Tax Act provides for an allowance of Rs. 800 per month (Rs. 9,600 per year).
2. It's an allowance that must be a part of your salary structure and designated as such in the salary sheet.
3. It's an allowance and not a reimbursement, so it has nothing to do with what you actually spend. If you were to walk from home to the office, you would still be able to claim the amount of Rs. 9,600 per year.
4. Business Expenses - That is conveyance related to the business of the employer (e.g., going from the office to the client's office, delivery, etc.) is an allowable deduction from the client's income tax dues. If the company spends that money, they will get a tax benefit; you as an employee will not be able to claim it.
5. If the company is reimbursing your expenses on travel, that amount must be at actuals, against vouchers that you give to accounts and get cash (or a transfer to your salary) and preferably not with your salary.
With reference to your particular query, if the actual travel expense from home to the office is not in your salary structure or CTC, you cannot ask your company to pay it. You can negotiate for it to be a part of your next increment perhaps. And there is no way for you to claim it from income tax either. Furthermore, you cannot now ask your employer to pay you a lesser salary and pay your petrol bills separately as a reduction in salary is definitely going to be scrutinized.