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pinki

· started a discussion

· 1 Months ago

solve (Question:107653.0)

plz ellaborate

Question:

Kareena, Ajay and Arjun started out on a journey to watch the newly released movie “Satryagarh”, which was being shown at wave cine-multiplex. The multiplex was 120 km away from their starting point of journey. Kareena and Arjun went by car at the speed of 50 km/h, while Ajay travelled by Tonga (horse cart) at 10 km/h. After a certain distance Arjun got off and travelled the rest distance by another Tonga at 10 km/h, while Kareena went back for Ajay and reached the destination at the same time that Arjun arrived. The number of hours required for the trip was:

Options:
A) 4 h
B) 5 h
C) 4.8 h
D) 6 h
Solution:
Ans: (c) 


Let A be initial point and B be destination

C is the point where Arjun got of from car

D is the point where Kareena pick up Ajay

Let (AD = x, CD= y, BC = z) then

If time are constant \(\cfrac{D_1}{S_1} = \cfrac{D_2}{S_2} \) 

Hence \(\cfrac{(AD + 2CD)}{50} = \cfrac{AD}{10}\)

\(\cfrac{x + 2y}{x}= \cfrac{5}{1}\) From Compenendo & Dividendo

\(\cfrac{2y}{x} = \cfrac{4}{1} \Rightarrow\cfrac{y}{x} = \cfrac{2}{1}\Rightarrow y = 2x\)

Similary

\(\cfrac{z + 2y}{z} = \cfrac{4}{1} \Rightarrow\cfrac{y}{z} = \cfrac{2}{1}\Rightarrow y = 2z\)

Hence y = 2x = 2z = k

Then x : y : z = 1 : 2 : 1

x + y + z = 120

k + k + 2k = 120 ⇒ k = 30

x = 30, y = 60, z = 30

Hence distance covered = x + y + y + y+ z

= 30 + 3 × 60 + 30 = 240 km.

Hence required time = \(\cfrac{240}{50} = 4.8\) hr. 

Knowledge Expert

· commented

· 1 Months ago

Dear student We are working on it and soon you will be updated. Keep learning Team TR
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