Two cities X and Y are connected by a regular bus service with a...

$\mathrm{t}_1=30 \mathrm{~min}=\frac{1}{2} \mathrm{hr}$$\begin{aligned} \mathrm{t}_2 & =10 \mathrm{~min}=\frac{1}{6} \mathrm{hr} \\ \mathrm{~V}_{\mathrm{B}} & =\text{ Speed\text{ of } Bus } \\ \mathrm{V}_{\mathrm{S}} & =\text{ Speed of scooty (girl) } \end{aligned}$$$(Same direction) (Opposite direction)$$\begin{aligned} & d=\left(V_B-V_S\right) t_1=\left(V_B+V_S\right) t_2 \\ & \Rightarrow\left(V_B-60\right) \frac{1}{2}=\left(V_B+60\right) \frac{1}{6} \\ & 3 V_B-180=V_B+ 60 \\ & 2 V_B=240 \\ & \Rightarrow V_B=120 \mathrm{~km} / \mathrm{hr} \text{ } \end{aligned}Distance $=\left(\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{S}}\right) \mathrm{t}_1\begin{aligned} & \mathrm{D}=(120-60) \frac{1}{2}=30 \mathrm{~km} \\ & \mathrm{t}=\frac{\mathrm{d}}{\mathrm{~V}_{\mathrm{B}}}=\frac{30}{120}=\frac{1}{4} \mathrm{hr}=15 \mathrm{~min} \text{ } \end{aligned}$$$