# Crack IBPS PO : Aptitude day 76 :

# Time and Work

## Target SBI PO : Aptitude Day 31

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Target SBI PO : Day 31

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- Question 1 of 10
##### 1. Question

1 pointsCategory: AptitudeP, Q and R can complete a piece of work in 6, 12 and 24 days respectively. P and R started working and Q joined them after one day. R left 2 days before completion of the work. In how many days was the work finished?

CorrectP’s 1 day’s work =1/8

Q’s 1 day’s work =1/12

R’s one day’s work =1/24

Let the number of days taken be x

Then,

x/6+(x-1)/12+(x-2)/24=1

7x-4 = 24

x = 4 days.

IncorrectP’s 1 day’s work =1/8

Q’s 1 day’s work =1/12

R’s one day’s work =1/24

Let the number of days taken be x

Then,

x/6+(x-1)/12+(x-2)/24=1

7x-4 = 24

x = 4 days.

- Question 2 of 10
##### 2. Question

1 pointsCategory: AptitudeThree pipes P, Q and R can fill a tank in 18, 24 and 32 minutes respectively. The pipe P is closed 9 minutes 15 seconds before the tank is filled. (Approximately) What time will the tank be full?

CorrectLet the tank be full in x minutes

9 minutes 15 seconds = 9.25 minutes

Therefore,

(x-9.25)/18+x/24+x/32=1

16x – 148+12x + 9x = 288

37x = 436 =>x=11.78~12

X=12 minutes.

IncorrectLet the tank be full in x minutes

9 minutes 15 seconds = 9.25 minutes

Therefore,

(x-9.25)/18+x/24+x/32=1

16x – 148+12x + 9x = 288

37x = 436 =>x=11.78~12

X=12 minutes.

- Question 3 of 10
##### 3. Question

1 pointsCategory: AptitudePipe A can fill the tank in 40 hours when it works at 40% of its efficiency. Pipe B is 5/6

^{th}as efficient as pipe A. How long will it take If both the pipe operate simultaneously at their 100% efficiency?CorrectPipe A can fill the tank when its efficiency is 100% =40×40/100=16 hours

Pipe B can fill the tank in 48 hours.

When both the pipes operate simultaneously.

Time =(48×16)/(48+16)=12 hours.

IncorrectPipe A can fill the tank when its efficiency is 100% =40×40/100=16 hours

Pipe B can fill the tank in 48 hours.

When both the pipes operate simultaneously.

Time =(48×16)/(48+16)=12 hours.

- Question 4 of 10
##### 4. Question

1 pointsCategory: AptitudeThe amount of work to be done in a company is increased by 80%. By what percentage is it necessary to increase the number of workers to complete the new work in the same time as before if the new workers are 100% more efficient?

CorrectLet initially 100 units of work were done by 100 workers in 1 day, so efficiency of each worker was 1%

Now the work becomes 180 units.

So, they need to complete 180 units of work in 1 day.

So, the 100 workers do the 100 units of work

The remaining x new workers need to this 80 units of work in 1 day whose efficiency is 200%each

So, number of new workers needed =80/2=40 newworkersneeded.

So, percent by which workers need to be increased =40/100×100=40%

IncorrectLet initially 100 units of work were done by 100 workers in 1 day, so efficiency of each worker was 1%

Now the work becomes 180 units.

So, they need to complete 180 units of work in 1 day.

So, the 100 workers do the 100 units of work

The remaining x new workers need to this 80 units of work in 1 day whose efficiency is 200%each

So, number of new workers needed =80/2=40 newworkersneeded.

So, percent by which workers need to be increased =40/100×100=40%

- Question 5 of 10
##### 5. Question

1 pointsCategory: AptitudeX and Y can complete a task in 45 days, when working together. After X and Y have been working together for 10 days, Y is called away and X, all by himself completes the task in the next 12 days. Had X been working alone, the number of days taken by him to complete the task would have been

CorrectBoth X and Y can do work in 45 days.

So work done in 1 day =1/45 th work

In 10 days, work done =1/45×10=2/9 work

In 12 days, work done by X alone =1-2/9=7/9 work

In 1 day , X can do =7/(9×12)=7/108 =>108/7=15 3/7

So, days X will take to complete whole work = 15 3/7 days

IncorrectBoth X and Y can do work in 45 days.

So work done in 1 day =1/45 th work

In 10 days, work done =1/45×10=2/9 work

In 12 days, work done by X alone =1-2/9=7/9 work

In 1 day , X can do =7/(9×12)=7/108 =>108/7=15 3/7

So, days X will take to complete whole work = 15 3/7 days

- Question 6 of 10
##### 6. Question

1 pointsCategory: AptitudeWater flows into a reservoir which is 300 m long and 250 m wide, through a pipe of cross-section (0.4m x 0.3m) at 30 kmph. In what time will the water level be 6 meter?

CorrectVolume of water collected in the tank in 1 hour

0.4×0.3×30×1000=3600 cubic meter

If after t hours, the water is at height of 6m,

3600t=300×250×6

t =

**125 Hours.**IncorrectVolume of water collected in the tank in 1 hour

0.4×0.3×30×1000=3600 cubic meter

If after t hours, the water is at height of 6m,

3600t=300×250×6

t =

**125 Hours.** - Question 7 of 10
##### 7. Question

1 pointsCategory: AptitudeA work is done by three person A, B and C. A alone takes 20 hours to complete a single product but B and C working together take 8 hours, for the completion of the same product. If all of them worked together and completed 21 products, then how many hours have they worked?

CorrectAs given in the question,

1/A=1/20;

1/B+1/C=1/8;

1/B+1/C+1/A=1/8+1/20=7/40;

In 40 hours, working together, they will complete 7 products.

Thus, in

**120 hours**they will complete 21 products.IncorrectAs given in the question,

1/A=1/20;

1/B+1/C=1/8;

1/B+1/C+1/A=1/8+1/20=7/40;

In 40 hours, working together, they will complete 7 products.

Thus, in

**120 hours**they will complete 21 products. - Question 8 of 10
##### 8. Question

1 pointsCategory: AptitudeThree men and three women can do a job in 6 days. When four men and five women work on the same job, the work gets completed in 5 days. How many days will a woman take to do the job, if she works alone on it?

CorrectFrom the question,

(3 men+3 women)×6 days =(4 men +5 women)×5 days.

18 men days +18 women days =20 men days +25 women days

⇒2men days =7women days

⇒ total work,

=18 men days +18 women days

=18×(7/2) womendays+18 womendays

= 63 women days +18 women days

=81 women days

Time taken by 1 women is 81 days

IncorrectFrom the question,

(3 men+3 women)×6 days =(4 men +5 women)×5 days.

18 men days +18 women days =20 men days +25 women days

⇒2men days =7women days

⇒ total work,

=18 men days +18 women days

=18×(7/2) womendays+18 womendays

= 63 women days +18 women days

=81 women days

Time taken by 1 women is 81 days

- Question 9 of 10
##### 9. Question

1 pointsCategory: AptitudeA bath can be filled by the cold water pipe in 30 min and by hot water pipe in 60 min (independently each). A person leaves the bathroom after turning on both pipes simultaneously and returns at the moments when the bath should be full. Finding, however, that the waste pipe has been open he now closes it. In 10 min more, bath is full. In what time would be the waste pipe empty it?

CorrectLet us assume some time l.c.m. (30, 60)min=60 min

Now in 30 min time cold water pipe will fill the bath 60/30=2 times whereas hot water pipe will fill it 60/60=1 times.

So in 60 min time bath will be filled 2+1=3 times.

So emptied bath will be fully filled in 60/3=20 min time if waste pipe is closed.

Initially waste pipe is opened, after 20 mins is passed and waste pipe is closed it takes 10 more minutes to fill the bath fully.

So waste pipe has emptied the 10/20=1/2 part of bath in 20 mins.

Rest 1/2 part of tank can be emptied by the waste pipe in 20/2=10 mins.

So waste pipe would empty the tank in 20+10=

**30 mins**IncorrectLet us assume some time l.c.m. (30, 60)min=60 min

Now in 30 min time cold water pipe will fill the bath 60/30=2 times whereas hot water pipe will fill it 60/60=1 times.

So in 60 min time bath will be filled 2+1=3 times.

So emptied bath will be fully filled in 60/3=20 min time if waste pipe is closed.

Initially waste pipe is opened, after 20 mins is passed and waste pipe is closed it takes 10 more minutes to fill the bath fully.

So waste pipe has emptied the 10/20=1/2 part of bath in 20 mins.

Rest 1/2 part of tank can be emptied by the waste pipe in 20/2=10 mins.

So waste pipe would empty the tank in 20+10=

**30 mins** - Question 10 of 10
##### 10. Question

1 pointsCategory: AptitudeGeorge Michael and John Glenn working alone, can complete a piece of work in 25 days and 30 days respectively. On day 1, John Glenn started the work and George Michael joined B from day 3 on-wards. Find after how many days will the work be completed?

CorrectFraction of work completed by George Michael in one day = 1/25

Fraction of work completed by John Glenn in one day = 1/30

Fraction of work completed by John Glenn on day1 and day 2 = 2(1/30)=1/15

Fraction of work left after 2 days = 1-1/15=14/15

Fraction of work completed by Both in one day = 1/25+1/30=11/150

Number of days after day 2 to complete work = (14/15)/(11/150)=140/11 days

So after 2+162/11 =14 8/11

**days**works will be completed.IncorrectFraction of work completed by George Michael in one day = 1/25

Fraction of work completed by John Glenn in one day = 1/30

Fraction of work completed by John Glenn on day1 and day 2 = 2(1/30)=1/15

Fraction of work left after 2 days = 1-1/15=14/15

Fraction of work completed by Both in one day = 1/25+1/30=11/150

Number of days after day 2 to complete work = (14/15)/(11/150)=140/11 days

So after 2+162/11 =14 8/11

**days**works will be completed.

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