Sir I have a 1250mah 25c battery.so it provides 31.25A(1250×25÷1000).I have a 30A esc so it pulls 30A from the battery . I know the the batteries A should be higher than esc's A but in this case batteries A is slightly higher so can I use the battery safely.please help me sir.

@nirup ms,

What does a 60c rating mean?
It means you can draw 60 amps from a 1000mah battery.
For how long?
For 1 minute, from full charge to zero, thereby killing off the battery.

What I've found over the last 10 years is:
1. The claimed C rating is far too optimistic
2. Drawing the rated current will make it puff up within a few cycles
3. Using only 10-12c from a 25-30C rated lipos helps them last several years
4. If not allowed to go below about 3.7v per cell in use, and
5. Provided they are stored at about 50% charge/3.85v when not in use.

Remember that drawing 30c from a 30c battery can only be done for one minute using up 50% of its capacity.

Please look at your question again.
1. Its not the Esc that pulls the current. Its the motor and prop combination
2. The Esc has to be rated somewhat greater than the max expected current draw, say a 30amp Esc for 20-25 amp draw (with airflow to cool the Esc)

So you have to consider:
1. How many amps will your motor/prop combo draw at full power
2. What will be the avg current, as it won't be full power all the time
3. Does your Esc have sufficient safety margin over the max expected draw
4. Can your battery provide the max expected current draw without exceeding say 10-15c
5. How long will you battery last, while supplying the avg reqd current, before using up say 50% of its capacity

I fear my reply may be far more than you expected.
The simple answer to your question 'can i use the battery safely' is 'it depends on the motor'
If the motor/prop combo draws 25amps, your Esc will get warm, but your battery will discharge in about 2minutes, and will be irrevocably dead in 3 minutes.

Hope you have a small motor
Regards

No. of Cells:       2 - 3 Li-Poly
  6 - 10 NiCd/NiMH 
  Kv:       1400 RPM/V 
  Max Efficiency:       78% 
  Max Efficiency Current:       6 - 12A (>75%) 
  No Load Current:       0.7A @10V 
  Resistance:       0.065 ohms 
  Max Current:       16A for 60S 
  Max Watts:       180W 
  Weight:       51.5 g / 1.82 oz 
  Size:       27.8 mm x 31 mm 
  Shaft Diameter:       3.2 mm 
  Poles:       14 
  Model Weight:       300 - 800g / 10.5 - 28.2 oz

Sir is the information of my motor. And I use a 30a Simone esc. So can I use  the battery safely.and how much flight time do I get.

@nirup ms,

You now have to find a prop which will not draw over 16 amps at full throttle, and draws 10-12 amps at 75-80% throttle.

If you have a wattmeter, you can check this with various props.
If not, I suggest an 8x4 prop to start with. (This will not overload your battery)

Charge your lipo fully. (Should show at least 4.15v per cell)
Run the motor with this prop at about 75% throttle for 3 minutes.
Stop motor, disconnect battery and check voltage.
If it is about 3.85v per cell, it means that this load (ie, this motor/prop combo at this throttle) used up 50% of the battery's capacity in 3 minutes.
Try to avoid going below 3.7v per cell when disconnected. (At that stage each cell will go to 3.5v or less under load)
Hope you have a lipo voltage checker that shows each cell voltage separately and not just total.
Best of luck.

Thank u sir for ur help.