NEET (UG) 2025 — Question 20

$\mathrm{t}_{1}=30 \mathrm{~min}=\frac{1}{2} \mathrm{hr}$

$\mathrm{t}_{2}=10 \mathrm{~min}=\frac{1}{6} \mathrm{hr}$

$V_{B}=$ Speed of Bus

$\mathrm{V}_{\mathrm{S}}=$ Speed of scooty (girl)

(Same direction) (Opposite direction)

$\mathrm{d}=\left(\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{S}}\right) \mathrm{t}_{1}=\left(\mathrm{V}_{\mathrm{B}}+\mathrm{V}_{\mathrm{S}}\right) \mathrm{t}_{2}$

$\Rightarrow\left(\mathrm{V}_{\mathrm{B}}-60\right) \frac{1}{2}=\left(\mathrm{V}_{\mathrm{B}}+60\right) \frac{1}{6}$

$3 \mathrm{~V}_{\mathrm{B}}-180=\mathrm{V}_{\mathrm{B}}+$ 60 $2 \mathrm{~V}_{\mathrm{B}}=240$

$\Rightarrow \mathrm{V}_{\mathrm{B}}=120 \mathrm{~km} / \mathrm{hr}$ Ans.

Distance $=\left(V_{B}-V_{S}\right) t_{1}$

$\mathrm{D}=(120-60) \frac{1}{2}=30 \mathrm{~km}$

$\mathrm{t}=\frac{\mathrm{d}}{\mathrm{V}_{\mathrm{B}}}=\frac{30}{120}=\frac{1}{4} \mathrm{hr}=15 \mathrm{~min}$