Q1. 
Two friends $A$ and $B$ run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. $A$ who runs faster laps $B$ in the middle of the $5^{th}$ round. If $A$ and $B$ were to run a 3 km race long race, how much start, in terms of distance, should $A$ give $B$ so that they finish the race in a dead heat? 
A.  545.45 metres 

B.  666.67 metres 

C.  857.14 metres 

D.  Cannot be determined 
Q2. 
Yana and Gupta leave points $x$ and $y$ towards $y$ and $x$ respectively simultaneously and travel in the same route. After meeting each other on the way, Yana takes 4 hours to reach her destination, while Gupta takes 9 hours to reach his destination. If the speed of Yana is 48 km/hr, what is the speed of Gupta? 
A.  72 kmph 

B.  39 mph 

C.  32 kmph 

D.  None of these 
Q3. 
Twenty six men  1,2,3,....25 and 26 participate in 10km running race on a circular track of length 100m. All of them start at the same time, from the same point and run in the same direction. Their speeds, taken in the order, are in increasing $AP$. The time taken by 26 to meet 1, for the first time after they start is 20 sec and the time taken by 13 to complete the race is 52 minutes and 5 seconds. Find the time taken (in seconds), for all the twenty six men to meet for the first time at the starting point. 
A.  1000 

B.  500 

C.  625 

D.  400 
Q4. 
A man driving his bike at 24 kmph reaches his office 5 minutes late. Had he driven $25%$ faster on an average he would have reached 4 minutes earlier than the scheduled time. How far is his office? 
A.  24 km 

B.  72 km 

C.  18 km 

D.  Data Insufficient 
Q5. 
Two motorists Anil and Sunil are practicing with two different sports car; Ferrari and Maclarun, on the circular racing track, for the car racing tournament to be held next month. Both Anil and Sunil start from the same point on the circular track. Anil completes one round of the track in 1 min and Sunil takes 2 min to complete a round. While Anil maintains speed for all the rounds, Sunil halves his speed after the completion of each round. How many times Anil and Sunil will meet between 6th round and 9th round of Sunil (6th and 9th round is excluded)? Assume that the speed of Sunil remains steady throughout each round and changes only after the completion of that round 
A.  382 

B.  347 

C.  260 

D.  None of these 