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(D) Let $V_B$ be the speed of the bus and $V_S = 60 \ km/h$ be the speed of the scooty.Let $d$ be the distance between two consecutive buses,given by

Vedclass · Accepted Answer

$15 \ min, 120 \ km/h$

Vedclass · Answer

(D) Let $V_B$ be the speed of the bus and $V_S = 60 \ km/h$ be the speed of the scooty.Let $d$ be the distance between two consecutive buses,given by $d = V_B 	imes T$.When the girl moves in the same direction as the bus,the relative speed is $(V_B - V_S)$. The time interval between buses passing her is $t_1 = 30 \ min = 0.5 \ h$.Thus,$d = (V_B - V_S) t_1 \implies V_B T = (V_B - 60) 	imes 0.5$  --- $(1)$When the girl moves in the opposite direction,the relative speed is $(V_B + V_S)$. The time interval is $t_2 = 10 \ min = 1/6 \ h$.Thus,$d = (V_B + V_S) t_2 \implies V_B T = (V_B + 60) 	imes (1/6)$ --- $(2)$Equating $(1)$ and $(2)$:$0.5(V_B - 60) = \frac{1}{6}(V_B + 60)$$3(V_B - 60) = V_B + 60$$3V_B - 180 = V_B + 60$$2V_B = 240 \implies V_B = 120 \ km/h$.Substitute $V_B$ into $(1)$:$120 	imes T = (120 - 60) 	imes 0.5$$120 	imes T = 60 	imes 0.5 = 30$$T = 30/120 = 0.25 \ h = 15 \ min$.

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