The correct option is A 45 minutes
Half past 6 means 6:30.
1 hour = 60 minutes
⇒ Number of minutes = (6 × 60) + 30 = 390 mins
Also, quarter to 6 means 5:45.
Number of minutes = (5 × 60) + 45 = 345 mins
So, the difference in their timings:
mins390−345––––––––45=45 minutes