Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour, if she travels 2 km by rickshaw and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 min longer. Find the speed of the rickshaw and of the bus.


Let the speed of the rickshaw and the bus are x and y km/h, respectively.

Now, she has taken time to travel 2 km by rickshaw,



she has taken time to travel remaining distance i.e., (14 - 2) = 12km


By bus


By first condition,


…(i)


Now, she has taken time to travel 4 km by rickshaw,


and she has taken time to travel remaining distance i.e., (14 - 4) = 10km, by bus =


By second condition,


…(ii)


Let and then Eqs. (i) and (ii) becomes


…(iii)


and …(iv)


On multiplying in Eq. (iii) by 2 and then subtracting, we get





Now, put the value of v in Eq. (iii), we get







Hence, the speed of rickshaw and the bus are 10 km/h and 40 km/h, respectively.


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