Q6. 
The $XYZ$ river flows at 12 km/hr. A boy who can row at $\frac{25}{18}$ m/s in still water had to cross it in the least possible time. The distance covered by the boy is how many times the width of the river $XYZ$? 
A.  2.1 

B.  2.3 

C.  2.6 

D.  2.9 
Q7. 
In a 3600 m race around a circular track of length 400m, the faster runner and the slowest runner meet at the end of the fourth minute, for the first time after the start of the race. All the runners maintain uniform speed throughout the race. If the faster runner runs at thrice the speed of the slowest runner. Find the time taken by the faster runner to finish the race. 
A.  36 minute 

B.  24 minute 

C.  16 minute 

D.  12 minute 
Q8. 
In an industry, the raw materials and the finished goods are transported on the conveyor belt. There are two conveyor belt, one for carrying parts from $P$ to point $Q$ and another for carrying parts from $R$ to point $Q$. $P$, $Q$ and $R$ in that order are in a straight line. Sometimes, the belt serves to transport cart, which can themselves move with respect to the belts. The two belts move at a speed of 0.5 m/s and the cart move at a uniform speed of 2 m/s with respect to the belts. A cart goes from point $P$ to $R$ and back to $P$ taking a total of 64 s. Find the distance $PR$ in meters. Assume that the time taken by the cart to turn back at $R$ is negligible? 
A.  48 

B.  54 

C.  60 

D.  64 
Q9. 
$P$ and $Q$ travels from $D$ to $A$ and break journey at $M$ in between. Somewhere between $D$ and $M$, $P$ asks "how far have we travelled?" $Q$ replies, "Half as far as the distance from here to $M$". Somewhere between $M$ and $A$, exactly 300 km from the point where $P$ asks the first question, "How far have we to go?" $Q$ replies, "Half as far as the distance from $M$ to here". The distance between $D$ and $A$ is: 
A.  250 km 

B.  350 km 

C.  450 km 

D.  500 km 
Q10. 
From a point $P$, on the surface of radius 3 cm, two cockroaches $A$ and $B$ started moving along two different circular paths, each having the maximum possible radius, on the surface of the sphere, that lie in the two different planes which are inclined at an angle of 45 degree to each other. If $A$ and $B$ takes 18 sec and 6 sec respectively, to complete one revolution along their respective circular paths, then after how much time will they meet again, after they start from $P$? 
A.  27 sec 

B.  24 sec 

C.  18 sec 

D.  9 sec 