Time and Work for SBI PO – 15

1) Aryan can do a piece of work in 16 days. Due to some problem, his efficiency reduces to 40%. Ankur’s efficiency also reduces to two-third his original efficiency. Now they can finish the work in 20 days. Then in how many days can Ankur and Aryan together finish the work at 100% efficiency?

a) 10 days

b) 15 days

c) 17 days

d) 12 days

e) None of these

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a) 10 days

When efficiency is 100% Aryan can finish the work in 16 days

When efficiency is 40% then, (16×100)/40=40 days

Ankur’s efficiency is two- third and they can finish the work in 20 days.

So, Ankur 1 day work = (1/20-1/40)days=1/40 days

So, Ankur finish the work in 40 days when efficiency is two-third his efficiency

So, When efficiency is 100% Ankur can finish the work in =(40×2)/3=80/3 days.

One day work by both of them when working at 100% efficiency =1/16+3/80=1/10

Total time taken to complete the work=10days.

2) Two pipes P and Q can fill a tank in 15 hours and 10 hours respectively. Another tap R can empty the full tank in 30 hours. All the three pipes were open for 2 hours. When it was remembered that the emptying pipe had been left opened. It was then closed. How much more time would it take to fill the tank?

a) 5 hours 16 minutes

b) 4 hours 24 minutes

c) 6 hours 14 minutes

d) 5 hours 12 minutes

e) None of these

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b) 4 hours 24 minutes

Total part of filled in 1 hour by the pipes P,Q and R =(1/15+1/10-1/30)=4/30

All three pipes are opened for 2 hours =(4/30×2)=4/15

Remaining =1-4/15=11/15

These parts are to be filled by pipes P and Q =(11/15×6)=22/5 hours.(1/15+1/10=1/6=6 hours.)

=4 hours 24 minutes.

3) Three men and four women earn Rs.5568 in 16 days. If seven men and six women earn Rs.7282 in 11 days then in how many days will five men and three women earn Rs.9545?

a) 23 days

b) 27 days

c) 30 days

d) 21 days

e) None of these

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a) 23 days

Let daily earnings of a man be `m` and woman be `w`.

Then 3m +4w =5568/16=348

And

7m +6w =7282/11=662

On solving equations, we get

M = 56 and w = 45

Now daily earnings of five men = 56×5 = 280

And daily earnings of three women = 45×3 =135.

Their total daily earnings = 280 +135 = 415

Required number of days =9545/415=23

4) Kabir was asked to finish testing of an application in 15 days which is generally completed by him a span of twenty days. His project manager asked his colleague Vikrant to help him in testing the application. This being a new application for Vikrant, he is only 80% as efficient as Kabir. Working together, they will be able to finish the testing in how many days?

a) 100/7 days

b) 125/3 days

c) 120/7 days

d) 150/7 days

e) None of these

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e) None of these

Kabir takes 20 days to complete the work.

Vikrant is 80 % as efficient as Kabir. Therefore, he can do the same work in 25 days.

Working together, they can complete the work in

=1/20+1/25

=9/100=100/9 days

5) X, Y and Z can together finish a job in 1 day. The efficiency of X is thrice that of Z and the efficiency of Y is twice that of Z. What is the ratio of the number of days taken by X and Y together to finish the job to the number of days taken by Y and Z together to finish the job?

a) 3 : 5

b) 5 : 7

c) 7 : 9

d) 5 : 3

e) None of these.

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a) 3 : 5

Let X, Y and Z take 2x, 3x and 6x days to finish the job alone.

Therefore, in one day they will complete, 1/2x ,1/3x,1/6x respectively.

Number of days taken by X and Y together to finish the job =1/(1/2x+1/3x)=6x/5

Number of days taken by Y and Z together to finish the job =1/(1/3x+1/6x)=6x/3

Required ratio = 3 : 5

6) Kohli, Dhoni and Yuvraj are three people who can complete a work in 10, 20 and 25 days respectively. What is the minimum number of days required to complete the work If not more than 2 people among them work on the same day and no 2 consecutive days have the same pair of people working?

a) 7 days

b) 12 days

c) 103/15 days

d) 89/16 days

e) None of these

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c) 103/15 days

Efficiency of kohli = 10 %

Efficiency of Dhoni = 5 %

Efficiency of Yuvraj = 4 %

So, Kohli + Dhoni = 15%, Dhoni +Yuvraj= 9% and Kohli + Yuvraj = 14%

To reduce the number of days we have to select the pair with more efficiency.

So, If we select Kohli + Dhoni and Kohli + Yuvraj alternatively We will get our value

So, 15+14+15+14+15+14 = 87% work is done in 6 days.

So, the remaining 13% can be done in 13/15 days by Kohli + Dhoni.

So, minimum number of days required is 6+13/15=103/15 days

7) Mohan, a resident of champa village can dig a well in 5 hours. He invites sohan and Rohan who can individually dig three-fourth as fast as he can to join him. He also invites Mohit and Rohit who can individually dig only one-fifth as fast as he can. If the five persons form a team and dig the same well and they start together, what is the total time taken by them to finish digging 29 such wells?

a) 40 hours

b) 25 1/3 hours

c) 50 hours

d) 35 hours

e) None of these

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c) 50 hours

Let the work be 100 units.

Mohan’s 1 hour work =100/5=20 units.

Sohan’s 1 hour work =3/4×20=15 units.

Rohan’s 1 hour work =3/4×20=15 units.

Mohit’s 1 hour work =1/5×20=4 units.

Rohit’s 1 hour work =1/5×20=4 units.

In one hour all five of them can do = 20+15+15+4+4 = 58 units of work.

Hence they can dig one well in 100/58 hours.

Time required to dig 29 such wells =29×100/58=50 hours

8) Ramesh can do a maths assessment consisting of 100 questions alone in 4 hours. Ramesh’s friends Surbhi and Alaka together can do the same set of questions in 1/3 speed of Ramesh. Pintu and Deepak together can do the same set of questions at 1/5 speed of Ramesh. If the five of them do the set of questions together, In how much time can they complete 230 set of questions?

a) 360 minutes

b) 580 minutes

c) 300 hours

d) 620 hours

e) None of these

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a) 360 minutes

Number of questions done by Ramesh in 1 hour =100/4=25

Number of questions done by Surbhi and Alaka in 1 hour =(25×1)/3=25/3

Number of questions done by Pintu and Deepak in 1 hour =25/5=5

In one hour, they can do 25+25/3+5=115/3 questions.

So they can do, 230 set of questions in(230/115)×3 = 6 hours.

9) Kolan can complete a work in 20 days and Renu can complete a work in 30 days. Both of them start the work together and then Solan joins them after some days and the total work is done in 9 days. After that they are paid a sum of Rs.1500. What is the share of Solan?

a) Rs.290

b) Rs.320

c) Rs.380

d) Rs.360

e) None of these

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e) None of these

Let us assure they do 100 units of work.

Efficiency of Renu=100/30=10/3%

Efficiency of Kolan=100/20=5%

Total efficiency =5+10/3=25/3%

Now as both of them work for all the 9 days then the percentage of work done by them would be =9×25/3=75%

The amount of work that is left to be done is = 100-75 = 25%

This 25% work is done by Solan.

So, Share of Solan in the amount of Rs.1500 =25/100×1500=Rs.375

10) A tank has two inlet pipes which can fill the empty tank in 12 hours and 15 hours working alone and one outlet pipe which can empty the full tank in 8 hours working alone. The inlet pipes are kept open for all the time but the outlet pipes was opened after 2 hours for one hour and then again closed for 2 hours then once again opened for one hour. This pattern of outlet pipes continued till the tank is get completely filled. In how many hours the tank has been filled, working on the given pattern?

a) 9 hours 30 minutes

b) 9 hours 10 minutes

c) 8 hours 25 minutes

d) 8 hours 40 minutes

e) None of these

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b) 9 hours 10 minutes

Efficiency of two inlet pipes A and B =100/12%+100/15%=15%

Efficiency of the outlet pipe C =100/8=12.5%

Now, Efficiency of two inlet pipes A and B along with an outlet pipe C

= 15%-12.5% = 2.5%

Tank filled in 3 hours = (15+ 15+ 2.5) = 32.5%

So, tank filled in 9 hours = (3×32.5) = 97.5%

Remaining = (100-97.5)% = 2.5%

On the 10th hour 2.5% will be filled by pipe A, B with its 15% efficiency.

Time taken =2.5/15=1/6 hours = 10 minutes.

Total time = 9 hours and 10 minutes

 

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