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Aniket Kumar

· started a discussion

· 1 Months ago

a (Question:146395.0)

hindi question fault

Question:
Balram travelled a total of 420 km in \(8\cfrac{1}{2}\) hours. He covered the first 180 km by train and the remaining distance by bus. Had he covered an additional 120 km by train and the remaining distance by bus, he would have taken 1 hour more for the journey. Find the speed of the train (in kmph).
Options:
A) 40
B) 45
C) 60
D) 30
Solution:

Ans (a) Let the speeds of his travel by train and bus be t kmph and b kmph respectively.

Then,  

\(\cfrac{180}{t}+\cfrac{420-180}{b}=8\cfrac{1}{2}\) i.e.  \(\cfrac{180}{t}+\cfrac{240}{b}=8\cfrac{1}{2}\)  ......(1)

\(\cfrac{180+120}{t}+\cfrac{240-120}{b}=8\cfrac{1}{2}+1\) i.e.

\(\cfrac{300}{t}+\cfrac{120}{b}=9\cfrac{1}{2}\)  ...........(2)

(1) \(\Rightarrow\) \(\cfrac{240}{b}=8\cfrac{1}{2}-\cfrac{180}{t}\)  and  

\(\Rightarrow\cfrac{120}{b}=9\cfrac{1}{2}-\cfrac{300}{t}\)  

\(\cfrac{240}{b}=2\left ( \cfrac {120}{b} \right )\)

\(\therefore 8\cfrac{1}{2}-\cfrac{180}{t}=2\left ( 9\cfrac {1}{2} -\cfrac{300}{t} \right )=19-\cfrac{600}{t}\)

\(\cfrac{420}{t}=10\cfrac{1}{2}\)

t = 40

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