Q.1 I and J starts running on the circular track in opposite directions.They start from a point M and meet for the first,second and third time at m & n respectively.What is the ratio of speeds of I and J ?
A) 2 : 1
B) 1 : 2
C) 2 : 3
D) 3 : 2
they meet 3 times in a circle so there ratio should be 2:1
Q.2 There are two points P and Q diametrically opposite on a circular road of circumference 20km. A car starts at P and makes 4 rounds. It starts of with a speed of 5km/hour and then increases its speed by 5km every time it reached Q. What is the interval between the 2nd time it passes through Q and the 4th time it passes through Q?
A) 8/3 hrs
B) 7 hrs
C) 7/3 hrs
D) 3 hrs
starting from 0 time to reach Q for the
1st time – 2hrs (at 5 kmph it would take 2hrs to cover 10 km)
2nd time – (2+2)hrs (at (5+5)kmph, it would take it further 2 hrs to cover a distance of 20km)
3rd time – (2+2+1+(1/3))hrs (at (10+5)kmph,it would take it futher 1+(1/3)hrs to come to Q)
4th time – (2+2+1+(1/3)+1)hrs (at (15+5)kmph,it would take it futher 1 hr to again come to Q)
thus the difference between the 4th and 2nd time is 1+1+(1/3) = 7/3 hrs
Q.3 A Lizard has to climb 40 feet on a tree. The Lizard climbs 1 foot in 1st day, 2 foot on second day, and so on. But every night it slides down half of the distance, which it climbed on the corresponding day. On which day will the Lizard climb on the tree ?
The distance covered by the Lizard forms a series with differences in AP with a common difference of 0.5.
1st day the distance travelled is 0.5, next day total distance from starting point is 1.5,3rd day total distance from starting point is 3,4th-5 and so on.
so differences are 1,1.5,2,2.5,3,3.5…….having a common difference of 0.5.
for n =12 distance covered from starting point is 39 feet from start.
Hence on 13th day it will climb on the tree.
Q.4 Two buses F and G are operated between cities I and J. One day F and G started from I and J respectively towards J and I respectively. After the two buses cross each other, the bus F takes 5 hours to reach city J and the bus G takes 3 hours 12 minutes to reach city I. After how much time from the start did the buses F and G cross each other.
A) 8 hours 12 minutes
B) 4 hours 24 minutes
C) 4 hours 6 minutes
D) 4 hours
Take t to be the required time. Same distance will be covered by F in 5 hours as that of G in t hours. Similarly, G in 16/5 hrs and F in t hours. Then compare the ratio of speeds, t/(16/5) = 5/t
Q.5 In a survey, it is found that in the year 2012 approximately1/3 of the airline passengers traveling to or from the Bangalore used airport A. If the number of such passengers that used airport B was 1/ 2 of the number that used airport A and 4 times the number that used airport C. If the survey consists of 37.3 unique passengers that used only one of these three airports, then the approximate number passengers (in millions) used airport C in that year is:
KA = 37.3/3 = 12.43
MA = KA/2 = 6.215
MA = 4 LA
LA = MA/4 = 6.215/4 = 1.55
2.0 is the closest approximation
Q.6 A stairway is 8 ft high such that each step accounts for half a foot upward & one-foot forward. An ant begins from ground level, What distance will it travel to reach the top of the stairway ?
Ant will travel 16 times upwards half a foot,
So upward distance travelled=16*0.5= 8ft
Also, the ant will travel 15 times a foot steps, so forward distance travelled= 15*1= 15ft
Total distance travelled 8+15 = 23 ft
Q.7 One-third of a journey was covered at a rate of 25 km per hour, one-fourth at the rate of 30 km per hour and the rest at the rate of 50 km per hour. Find the average speed of the whole journey.
A) 33 1/3 km/h
B) 66 1/3 km/h
C) 36 1/6 km/h
D) 63 1/3 km/h
Let the total distance of the journey be 12 km
Distance covered at the speed of 25 km/h = 4 km
Distance covered at the speed of 30 km/h = 3 km
Distance covered at the speed of 50 km/h = 5 km
Average speed = = = 33 km/h
Q.8 A Formula One driver covers some distance at the speed of 60 mph. With what speed should he return so that his average speed of the total journey comes out to be 120 mph?
A) 180 mph
B) 120 mph
D) Not possible
Using the funda that the average speed of a body can never be the double or more than any of the speed.
So the average speed cannot be 120 kmph. Hence, can’t possible.