Two cars (A and B) start at the starting line at the same time on a 3-mile long circular track, going in opposite directions. As they drive around the course, they pass each other many times. Exactly one hour after starting, they pass each other for the 33rd time. At this point car A has completed exactly 20 laps. What is the average speed of Car B?

Angad and Bali traveled on the same road and at the same rate from Delhi to Bhatinda. At the 50th milestone from Bhatinda, Angad overtook a herd of goats which were going at the rate of 1.5 miles per hour. Two hours after that Angad met a wagon which was moving at the rate of 2.25 miles per hour. Bali overtook the same herd of goats at the 45th milestone from Bhatinda, and met the wagon exactly 40 minutes before he came to the 31st milestone. How far away from Bhatinda was Bali when Angad reached Bhatinda?

One of the ski lifts at Kulu Manali climbs the mountain in a line that parallels one of the ski runs. Both the run and the lift are two km long, and a chair passes the starting point of the lift every 10 seconds. A skier starts her run just as the chair arrives at the top of the lift and another chair starts back down. She arrives at the bottom just as a chair is starting up the mountain and another chair is completing its descent. Counting these two chairs and the two at the start of her run, she sees 97 chairs on their way up the mountain and 61 chairs on their Way down. If the chair that started down the slope at the same time that the skier did is still on its way down when the skier reaches the bottom of the slope, what is the average speed of the skier?

the number of chairs that came out on the up line = number of chairs that went inside on the down line

so chairs on line = (97+61)/2 = 79 , So 18 chairs came up and 18 went inside by the time skier reached top to bottom, it took 170 sec, because 1st came up at 0 sec and then 10 sec gap

and hence skier took 170 sec to reach bottom

so 2 km is covered in 170 sec

At what time instant after 8 o' clock do the short hand and long hands of a clock enclose the equal angles with the horizontal?

horizontal line is the line connecting 3 and 9.

Let's say min hand is at x angle from 3, means it has traveled 90-x degrees. after 8 o clock.

and hour hand is at x angle before 9, means it has traveled 30-x in the same time.

now 90-x/(5.5) = 30-x/0.5

horizontal line is the line connecting 3 and 9.

Let's say min hand is at x angle from 3, means it has traveled 90-x degrees. after 8 o clock.

and hour hand is at x angle before 9, means it has traveled 30-x in the same time.

now (90-x)/(5.5) = (30-x)/0.5

Sir, I think speed of minute hand should be 6 instead of 5.5

one gains 2.5 mins and other loses 1.5 mins , hence they are 4 mins apart in an hour. So for 120 mins apart, it will take 30 hours.

Akbar & Birbal start together on a circular track of 600 m in opposite directions at 6m/s and 4m/s respectively. Every time they meet, they exchange their speeds as well as directions. Find out the shortest distance of their 7th meeting point from the starting point along the track.

Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/h. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2, respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and shyam’s return

to the point A is (2003)