Please clear the difference in terms.

Authorised capital is the maximum capital that can be issued to shareholders. then shareholders subscribe to these and pay money for issue of shares. This is paid-up capital. Paid-up capital will always be less than or equal to authorised capital but not more. You can increase the authorised capital. Sometimes on MCA website an increase in authorised capital is shown late and hence there can be a discrepancy 

Thank you Niral Gangar. So on what ratio is share allotted based on paid up capital paid by a director in case of private limited? Also, the company I am talking about is a big one and though pays less, hires over 300 people. So if they say the paid up capital is 2.5 crores then are they actually running their annual expenses such as rentals, salaries within this 2.5 crores only for that particular year? Could they be hiding some money?

Normally in a private company shares are allotted on Face value of Rs. 10/- at the time of incorporation  But big companies after incorporation issue further shares and the value could be anything (Rs. 1 to 1000+ also) based on its calculated share value. Payment of exps has nothing to do with its paid-up capital. I may have capital of 1 lakh but have income/ revenues of Rs. 1 Cr out of which I could pay entire 1 Cr for exps. Hope this clarifies