A) \[50kmph\]
B) \[25kmph\]
C) \[10kmph\]
D) \[24kmph\]
Correct Answer: D
Solution :
: Let S be distance between A and B. Let \[{{t}_{1}}\] be time taken by the car to move from A to B with speed \[{{v}_{1}}\] and \[{{t}_{2}}\] be time taken by the car to move from B to A with speed \[{{v}_{2}}\]. Then \[{{t}_{1}}=\frac{S}{{{v}_{1}}}\] and \[{{t}_{2}}=\frac{S}{{{v}_{2}}}\] Average speed of the car \[{{\text{v}}_{\text{av}}}\text{=}\frac{\text{Total}\,\text{distance}\,\text{travelled}}{\text{Total}\,\text{time}\,\text{taken}}\text{=}\frac{\text{2S}}{{{\text{t}}_{\text{1}}}\text{+}{{\text{t}}_{\text{2}}}}\] \[=\frac{2S}{\frac{S}{{{v}_{1}}}+\frac{S}{{{v}_{2}}}}=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\] Here, \[{{\text{v}}_{1}}=30\text{ }kmph\], \[{{\text{v}}_{2}}=20\text{ }kmph\] \[\therefore \] \[{{v}_{av}}=\frac{2\times 30\times 20}{30+20}=24kmph\]
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