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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. Find the speed of the rickshaw and of the bus.

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a

20 km/hr, 40 km/hr

b

20 km/hr, 30 km/hr

c

10 km/hr, 40 km/hr

d

10 km/hr, 20 km/hr

answer is C.

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Detailed Solution

As it is given that Ankita travels 14km to her home partly by rickshaw and partly by bus. Let us find the speed of both vehicles
Let us consider that the speed of rickshaw and bus be x and y Km/hr respectively.
Then according to the question distance covered by bus

= 14 −

distance covered by rickshaw
Now, she takes half an hour if she travels

2

km by rickshaw, and the remaining distance by bus.
We get

2 x + 12 y = 12

……(1)
Also if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer.
We get,

4 x + 10 y = 3960

….(2)
On multiplying eq. (1) by 2 and subtract eq. (2) from (3), we get

4 x + 24 y = 1

….(3)

⇒ 24 y − 10 y = 1 − 3960 ⇒ 14 y = 2160 ⇒ y = 40

Substitute the value of y in eq. (1) we get

2 x + 1240 = 12 ⇒ 2 x = 12 − 310 ⇒ 2 x = 210 ⇒ x = 10

We get

x = 10, y = 40

Therefore, the final speed of rickshaw and bus is 10 km/hr and 40 km/hr.
Hence, the correct option is 3.

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