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Three professors Dr. Gupta, Dr. Sharma, Dr. Singh are evaluating answer script of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work. Dr. Gupta starts the evaluation work and works for 10 days and then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days and then stops. In how many days, Dr. Singh can complete the remaining evaluation work?

Option: 1

7.2 days


Option: 2

9.5 days


Option: 3

11.5 days


Option: 4

None

 


Let's solve this step by step

1)let's Dr.Singh's efficiency be x units/days

Then Dr.sharma = 20% more = 1.2x

          Dr.Gupta = 40% more than Sharma = 1.4 x 1.2x = 1.68x units/days

2) Dr.Gupta takes 10 days less than Dr.Sharma

    Time taken by sharma = S

     Then Gupta's time = S- 10 days

Work = Efficiency x Time

So , 1.2x x S = 1.68x x(S-10)

Cancel x :

1.2S = 1.68( S - 10 )

1.2S = 1.68S - 16.8

0.48s = 16.8

S = 35

So , Dr.Sharma takes 35 days

Dr.Gupta takes 25 days

3) find total work : using Dr.Gupta's rate and time :

Work = 1.68x x 25 = 42x units

4) work done by gupta 10 days = 1.68x x 10 = 16.8x

work done by Sharma in 15 days = 1.2x x 15 = 18x

Total work done = 16.8x + 18x = 34.8x

Remaining= 42x - 34.8x = 7.2x

5) Dr.Singh's rate = x

Time = Work /Rate = 7.2x / x = 7.2 days

Answer : Option 1 ( 7.2 days )

 

View Full Answer(1)
Posted by

Kavya S P

Aditya, Vedus and Yuvraj alone can do a job for 6 weeks, 9 weeks and 12 weeks respectively. They work together for 2 weeks. Then, Aditya leaves the job. Vedus leaves the job a week earlier to the completion of the work.The job would be completed in:

 

Option: 1

4 weeks


Option: 2

5 weeks


Option: 3

7 weeks


Option: 4

None


Aditya's 1 week work = 1/6

Vedus's = 1/9

Yuvraj's = 1/12

Step 1 : work done for first 2 weeks 

= 2 x (1/6 + 1/9 + 1/12 )

LCM of 6,9,12 = 36

= 2 x (6+4+3)/36 = 2 x 13/36 = 26/36

Remaining work = 1 - 26/36 = 10/36

Step 2  : after 2 weeks aditya leaves .vedus and yuvraj work together 

Let total time = x weeks

So vedus , works ( x - 3 ) weeks ( he leaves 1 week before ends )

Yuvraj works full ( x - 2 ) weeks 

Work done after Aditya left :

= ( x - 3 ) x 1/9 + (x-2) x 1/12

= (4x - 10 )/36

This must equal to remaining work:

(4x - 10 )/36 = 10/36

4x - 10 = 10

4x = 20

x = 5

Answer : option 2 - 5 weeks

 

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Posted by

Kavya S P

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In what time can Sonali cover a distance of 400 m, if she runs at a speed of 20 km/hr?

Option: 1

$1 \frac{1}{5}~min$


Option: 2

$1 \frac{1}{2} ~min$


Option: 3

$2~ min$


Option: 4

$3 ~min$


Given : 

Distance = 400 meters , 

Speed = 20 km/hr = 20000/60 = 333.33 meters/min

Time = Distance/speed

           = 400 / 333.33 ~ 1.2 minutes

            = 6/5 minutes

             = 1 1/5 minutes 

Answer : option 1 

           

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Posted by

Kavya S P

A man riding his bicycle covers 150 meters in 25 seconds. What is his speed in km/hr?

Option: 1

20 km/hr


Option: 2

21.6 km/hr


Option: 3

23 km/hr


Option: 4

25km/hr


Distance = 150 m

Time  = 25 s

Step 1  : speed in m/s = 150/25 = 6 m/s

Step 2 : convert km/hr = 6 x 18/5:=21.6 km/hr

Answer : option 2( 21.6 km/hr )

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Posted by

Kavya S P

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An athlete runs 200 meters race in 24 seconds. His speed is

 

Option: 1

20 km/hr


Option: 2

24 km/hr


Option: 3

28.5 km/hr


Option: 4

30 km/hr


28.5

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Posted by

Guru G

A train is moving with a speed of 30 m/s. Its speed is

Option: 1

72 km/h 


Option: 2

100 km/h


Option: 3

120 km/h


Option: 4

108 km/h

 


Given : 

Speed = 30 m/s

But you need to answer in kilometres per hour(km/h)

Step by step conversion

To convert m/s to km/h use this formula:

1 m/s = 18/5 km/h

So,

30 m/s = 30 x 18/5 = 540/5 = 108 km/h

Final answer : 108 km/h ( option 4)

Why multiply by 18/5

Because:

1 km = 1000 meters

1 hour = 3600 seconds 

1 m/s = 1000/3600 x km/h = 18/5 km/h

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Posted by

Kavya S P

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The distance between two stations A and B is 440 km. A train starts at 4 p.m. from A and move towards B at an average speed of 40 km/hr. Another train starts B at 5 p.m. and moves towards A at an average speed of 60 km/hr. How far from A will the two trains meet and at what time?

Option: 1

200,8 p.m.


Option: 2

300,9 p.m.


Option: 3

200,9 p.m.


Option: 4

300,8 p.m.


200,9

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Posted by

Guru G

PQ is a tunnel. A dog sits at the distance of 5/ 11 of PQ from P. The train whistle coming from any end of the tunnel would make the dog run. If a train approaches P and dog runs towards P the train would hit the dog at P. If the dog runs towards Q instead, it would hit the dog at Q. Find ratio of speed of train and dog?

 

Option: 1

5:2


Option: 2

16:5


Option: 3

11:1


Option: 4

34:3


Option 3 - 11:1

########            P____5_____¶______6_____Q

"¶" is the dog located inside the tunnel PQ and #####... is a train approaching to it. 

Case 1 - Dog decides to reach point P 

Distance covered by Dog - 5 parts and train reaches at P

Case 2 - Dog decides to run towards point Q

At the time train reaches to point P, the dog covers 5 parts in direction of Q. Now the left out part covered by dog will be 1 part towards Q .

At the time dog covers 1 part and reaches Q, train covers whole 11 parts of tunnel and reaches from P to Q. 

So, 11 part of train is eual to the 1 part covered by the dog to reach Q. 

Ratio of their speeds - Train:Dog = 11:1  

 

 

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Posted by

Vaibhavi Gupta

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A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the

A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water

  • Option 1)

    15 km/hr

  • Option 2)

    11 km/hr

  • Option 3)

    13 km/hr

  • Option 4)

    14 km/hr

  • Option 5)

    12 km/hr

View Full Answer(1)
Posted by

rishi.raj

A man can row 40 kmph in still water and the river is running at 10 kmph. If the man takes 1 hr to

Option 5

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Posted by

Affan

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE
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