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soumya

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· 1 Months ago

explanation (Question: 117295.0 )

plaese give a detailed explanation of the same

Question:

Every day, Han drives his motorcycle at a certain speed and reaches his office exactly on time. One day, after travelling a certain distance, he slowed down to 3/4th of his initial speed and arrived at his office 6 minutes late. Had he slowed down to 2/3rd of his initial speed 6 km further on, he would still have reached 6 minutes late. What is his initial speed?       

Options:
A) 36 km/hr 
B) 46 km/hr    
C) 60 km/hr  
D) 72 km/hr
E) 52 km/hr
Solution:
 Let the usual speed and time be s and t respectively 

Now, A is the point where he charges his speed.


\(\cfrac{3}{4}s\times\cfrac{4}{3}t\)    {∵ s × t = constant}

\(\Rightarrow\) \(\cfrac{4}{3}\) t - t = 6 min

\(\cfrac{t}{3}=6 \) min, t = 18 min (normal time)

2nd case


\(\cfrac{2}{3}s\times\cfrac{3}{2}t\)

\(\Rightarrow\) \(\cfrac{3}{2}\) t - t = 6

t = 12 min (normal time)

time taken to cover distance b/w A and B = 18 - 12 = 6 min

 s = \(\cfrac{D}{t}\) = \(\cfrac{6 km}{6 min} \times 60\) = 1 \(\times\) 60 km/hr

= 60 km/hr

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