Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km / h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
D. 15 ~min , 120 ~km / h
t _1=30 ~min = 1 2 hr aligned t _2 & =10 ~min = 1 6 hr \\ ~V _ B & = Speed of Bus \\ V _ S & = Speed of scooty (girl) aligned (Same direction) (Opposite direction) aligned & d= (V_B-V_S ) t_1= (V_B+V_S ) t_2 \\ & (V_B-60 ) 1 2 = (V_B+60 ) 1 6 \\ & 3 V_B-180=V_B+ 60 \\ & 2 V_B=240 \\ & V_B=120 ~km / hr aligned Distance = ( V _ B - V _ S ) t _1 aligned & D =(120-60) 1 2 =30 ~km \\ & t = d ~V _ B = 30 120 = 1 4 hr =15 ~min aligned
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