Practise Tests
11
Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?
Answer : Option D
Explanation:
Let us assume Car A travels at a speed of a and Car B travels at a speed of b. Further, let us assume that they meet after t minutes.
Distance traveled by car A before meeting car B = a * t. Likewise distance traveled by car B before meeting car A = b * t.
Distance traveled by car A after meeting car B = a * 54. Distance traveled by car B after meeting car A = 24 * b.
Distance traveled by car A after crossing car B = distance traveled by car B before crossing car A (and vice versa).
=> at = 54b ---------- (1)
and bt = 24a -------- (2)
Multiplying equations 1 and 2
we have ab * t2 = 54 * 24 * ab
=> t2 = 54 * 24
=> t = 36
So, both cars would have traveled 36 minutes prior to crossing each other. Or, B would have taken 36 + 24 = 60 minutes to travel the whole distance. Choice (A).
Correct Answer: 60
12
Two trains A and B are 100 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
Answer : Option B
Explanation:
Speed of A = 15 m/s
Speed of B = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 6 s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 100 + 150 = 250 m. Time taken = 10 seconds
13
Two trains left from two stations P and Q towards station Q and station P respectively. 3 hours after they met, they were 675 Km apart. First train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take the first train to make the whole trip?
Answer : Option C
Explanation:
Total distance travelled by both the trains before meeting = D. This distance will be covered in the proportion of their speeds. Clarify with the diagram.
3 hours after meeting distance travelled by A = SA x 3 and by B = SB x 3
Therefore, 3 (SA + SB) = 675 =) SA + SB = 225.
Now the remaining distance to be covered by first train is DSB/(SA + SB). Therefore, time taken = DSB(SA+SB)SA=16 ---------- (1)
Similarly, DSA(SA+SB)SB=25 ---------- (2)
Dividing equation 1 by 2 -
S2AS2B=2516=>SASB=54. Therefore, SA+45∗SA=225 => SA = 125 Km/hr and SA = 100 Km/hr
From equation 2, DSA=16∗(SA+SB)SB=16∗225
14
Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?
Answer : Option C
Explanation:
Arun has travelled 60 km when Barun starts.
Barun overtakes Arun in 60/(40 – 30) = 6 hrs
In this time, Barun travels 6 × 40 = 240 km from the starting point.
Kiranmala overtakes Arun at the same point.
Kiranmala takes 240/60 = 4 hrs to reach there.
Arun takes 240/30 = 8 hrs to reach there.
∴ Kiranmala starts 8 – 4 = 4 hrs after Arun. Hence, option 3.
15
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Answer : Option C
Explanation:
Let the rate upstream of the boat
=x kmph
and the rate downstream of the boat =y kmph
Distance travelled upstream in 8 hrs 48 min = Distance travelled downstream in 4 hrs.
Since distance = speed × time, we have
x×845=y×4x×445=y×4x×115=y?(equation 1)
Now consider the formula given below
Speed in still water =12(a+b) km/hr
Rate of stream =12(a−b) km/hr
[Read more ...]
Hence, speed of the boat =y+x2
speed of the water =y−x2
Required Ratio
=(y+x2):(y−x2) =(y+x):(y−x)
=(11x5+x):(11x5−x) (? Substituted value of y from equation 1)
=(11x+5x):(11x−5x)
16
Two trains start at the same time from two stations A and B towards each other. They arrive at B and A respectively in 25 hours and 16 hours after they have passed each other. If the speed of the train that started from A is 60 kmph, then what is the speed of the second train is?
17
A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction.how much time does it take for the train to pass the jogger?
18
The North-South Express is a pair of trains between Jammu and Chennai. A train leaves Jammu for Chennai exactly at 12 noon everyday of the week. Similarly, there's a train that leaves Chennai bound for Jammu on everyday of the week exactly at 12 noon. The time required by a train to cover the distance between Chennai and Jammu is exactly 7 days and 1 minute. Find the number of trains from Chennai to Jammu which a train from Jammu to Chennai would cross in completing its journey, assuming all the trains are on time.
Answer : Option D
Explanation:
Let a train from Chennai to Jammu starts on Day 1 and it reaches jammu on day 8 at 12:01 Hrs
The train which starts from Jammu on Day 8 at 12:00 will cross this Day 1 train (from Chennai) at approx. 12:00:30 Hrs and this train will reach Chennai on day 15 at 12:01 Hrs so it will cross the train which started from Chennai at 12:00 Hrs on day 15 (in between 12:00 Hrs and 12:01 Hrs).
So it will cross a total of 15 trains.
19
Abhishek started from Bangalore to kysore and Aishwarya from opposite direction. They met at a resturant mid way and had lunch for 30 minutes. Abhishek travelled 180 km more than Aishwarya. After they departed Abhishek took 2 hrs to reach Mysore and Aishwarya 4.5 hours. If they travelled with uniform speed. wat will be the distance between two cities?
Answer : Option B
Explanation:
There is a small proof that can be helpful for this particular question.
The ratio of times after meeting will be the square of the reciprocal of the ratio of the speeds
So, Aishwarya's time/Abhishek's time = (speed of abhishek)^2/ (speed of aishwarya) ^ 2
The other proof that will help is the time for which they travelled before meeting will be square root of the product of two times
So, from the first one ratio of their speed is 1.5
From the second one, they travelled for 3 hours before meeting
In three, hours with 1.5 times speed abhishek travelled 180 km more.
As the ratio of the distances is also 1.5(based on the speeds), their distances are 540 and 360
As they together covered the total distance , the total distance is 900
Answer is 900
Time Ratio=(2/4.5)^1/2=2:3
Speed Ratio=3:2
Let X is the total Distance therefore,
3X/5-2X/5=180
X=900
20
Two trains A and B seperated by a distance of 1200m approach each other at 30m/min.A bird flying at 60 m/min flies from train A to B, returns to A flies back to B and so on till the trains meet.
What is the total distance travelled by the bird?
How many trips between the train does the bird make in all?
Answer : Option A
Explanation:
Time taken by trains before meeting = 1200/(30+30)= 20 mins
Distance travelled by bird during this time = 20*60=1200 mtrs
Brainwiz
Thank you for choosing BRAINWIZ. Our team will contact you soon.