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Q.

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 minutes longer. Then what are the respective speeds of the rickshaw and the bus?


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a

25 km/h, 25 km/h

b

20 km/h, 30 km/h

c

15 km/h, 35 km/h

d

10 km/h, 40 km/h 

answer is D.

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Detailed Solution

It is given that 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 minutes longer.
Given, total distance traveled by Ankita = 14 km.
Let the speed of the rickshaw be x and the speed of the bus be y.
The expression for the speed of the object is, s= D t   . Here, s is speed, D is the distance and t is the time taken.
So, according to the question, we get,
2 x + 12 y = 1 2          ....  1   And,
4 x + 10 y = 1 2 + 9 60 ⇒ 4 x + 10 y = 39 60             ....  2  
On multiplying the equation (1) by 2, we get,
  4 x + 24 y = 2 2 ⇒ 4 x + 24 y =1    ....  3  
Now, we subtract equation (3) from equation (2), we get,
24 y − 10 y =1− 39 60 ⇒ 14 y = 21 60 ⇒y= 840 21 ⇒y=40  
From substituting the value of y = 40 for x in the equation (1), we get,
2 x + 12 40 = 1 2 ⇒ 2 x =0.2 ⇒x=10  
The speed of the rickshaw and bus is 10 Km/h  and 40 Km/h   respectively.
Hence, the correct option is 4.
 
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