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Q:

Arjun and Bhishma are running on a circular track of length 600m. Speed of Arjun is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?

Answer

Sol : Time = Circumference Relative Speed = 60010 = 60 sec.


 


Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.


 


Since , they make  a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.

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Subject: Time and Distance Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

In a one km race A gives B a start of 100m and in a one km race B gives a start of 80 m to C. In a 1 km race who will win and by how much distance from the worst performer between two losers?

Answer

Ratio  of speeds of A:B = 1000:900 = 100:90


Ratio of speeds of B:C = 1000:920 = 100:92


Therefore, when A moves 1000m , B moves 900 m and when B moves 900m, C moves 828m


Thus,             


Since , C moves 8 % less than B in the same time . Thus, C is the worst performer and A will win by him by 172 m

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Subject: Time and Distance

Q:

A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the rate of stream of the river ?

Answer

\inline \frac{Time\: taken\: in\: upstream}{Time\: taken\: in\: downstream} = \inline \frac{2}{1}


 \inline \therefore \inline \frac{Downstream\: speed}{upstream\: speed} = \inline \frac{2}{1}        where  \inline \frac{B+R}{B-R}=\frac{2}{1}


B ---> speed of boat in still water


R---->speed of current


\inline \Rightarrow \frac{B}{R}=\frac{3}{1}    ( By componendo and dividendo)


\inline \Rightarrow \frac{9}{R}=\frac{3}{1}\: \: \Rightarrow R= 3\: km/h

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Subject: Boats and Streams

Q:

A train of length 250 m crosses a bridge of length 150m in 20 seconds. What is the speed of train?

Answer

Sol : (length of train+ length of bridge) = speed of train x Time


        (250+150) = 20 x Speed


        Speed = 400/20= 20 m/s =72 km/h

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Subject: Time and Distance

Q:

A contractor  undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor calculated that  he needed to increase 5 additional  men every 2 days to complete the work in the time the client wanted it:

If the work was further increased by 50% but the contractor continues to increase the 5 workers o every 2 days then how many more days are required over the initial time specified by the  client.

A) 1 day B) 2 days
C) 5 days D) None of these
 
Answer & Explanation Answer: B) 2 days

Explanation:

Total work = 100+50 = 150man-days

In 8 days 100 man-days work  has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man- days work. Thus the work requires 2 more days.

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Filed Under: Time and Work

Q:

In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap. If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of  efficiency of 8th tap and 12th tap, respectively?

A) 4:1 B) 5:3
C) 16:1 D) 1:16
 
Answer & Explanation Answer: D) 1:16

Explanation:

Time taken by 8th tap = 2 x 2 x 2= 8 hours

Time taken by 12th tap = 2x (1/2) x (1/2)  = 1/2 hour

Ratio of time taken by 8th tap and 12th tap = 8 : 1/2 =16:1

Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16

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Filed Under: Time and Work

Q:

A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed.

If there is a lekage also which is capable of draining out the liquid from the tank at half of the  rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?

A) 3 hours B) 4 hours
C) 5 hours D) None of these
 
Answer & Explanation Answer: B) 4 hours

Explanation:

Rate of leakage = 8.33% per hour

Net efficiency = 50 - (16.66 + 8.33)= 25%

Time required = 100/25 = 4 hours

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Filed Under: Time and Work

Q:

Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?

A) 4:18 pm B) 3:09 pm
C) 12:15 pm D) 11:09 am
 
Answer & Explanation Answer: B) 3:09 pm

Explanation:

Efficiency of P= 100/20= 5% per hour  

Efficiency of Q= 100/25= 4% per hour  

Efficiency of R= 100/40= 2.5% per hour  

Efficiency of S=100/50= 2% per hour 

 

Cistern filled till 10 am by P, Q and R  

Till 10.00am Pipe P filled 20%Till 10.00am Pipe Q filled 8%Till 10.00am Pipe R filled 2.5%30.5%  

Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern. 

Rest of cistern to be filled = 100 - 30.5 = 69.5%  

 

Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern 

= 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx).

Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins

 

It means cistern will be filled up at 3:09 pm

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Filed Under: Time and Work