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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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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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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

Q:

A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?

A) 50 B) 40
C) 45 D) 10
 
Answer & Explanation Answer: D) 10

Explanation:

Let the number of workers be x.

Now, Using work equivalence method,

X + (X-1) + (X-2)+ . . . . + 1 = X *55% of X

 

=> [X * (X+1)] / 2 = X * (55X/100)    [because, Series is in AP. Sum of AP = {No. of terms (first term+ last term)/2} ]

Therefore, X = 10 

 

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Q:

Mr. stenley employed a certain number of typist for his project. 8 days later 20% of the typist left the job and it was found that it took as much time to complete the rest work from then as the entire work needed with all the employed typists. The average speed of a typist is 20 pages/hour. Minimum how many typist could be employed? 

A) 10 B) 5
C) 15 D) 4
 
Answer & Explanation Answer: B) 5

Explanation:

Since 20% i.e 1/5 typists left the job. So, there can be any value which is multiple of 5 i.e, whose 20% is always an integer. Hence, 5 is the least possible value.

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Filed Under: Time and Work