Time and Work

Q.1) Roy and Paul are two workers working together they can complete the Whole work in 10 hours. If Roy worked for 2.5 hours and Paul worked for 8.5 hours. Still there was half of the work to be done. If Roy is working alone, then how much percent of the work is done by Roy in six hours?

a) 45%

b) 35%

c) 25%

d) 15%

e) None of these

b

According to the question,

2.5/Roy+2.5/paul+6/paul=1/2

2.5(1/Roy+1/Paul)+6/paul=1/2

2.5/10+6/paul=1/2

6/paul=1/2-1/4=1/4

Paul = 24 hours

1/Roy=1/10-1/24=7/120

Roy can complete the work in  120/7  hours

Work done by Roy in one hour = 7/120

Work done by Roy in six hour = 7/20

Required percentage = 7/20×100=35%

Q.2) A tank can be filled by two pipes P and Q in 18 minutes and 27 minutes respectively. If both the pipes are opened simultaneously such that the pipe P is opened first and pipe Q next to it. Thus, after how much time should pipe P be closed so that the unfilled part of the tank is filled in by pipe Q in 12 minutes?

a) 15 minutes

b) 12 minutes

c) 9 minutes

d) 6 minutes

e) None of these.

e

Let after x minutes pipes P will be closed

Then,

x/18+12/27=1

x/18=15/27

x=(18×15)/27=10 minutes.

Q.3) A, B and C working together can complete a work in  hours. If A works at half his own speed and C works at twice his own speed, the time taken to complete the work (all three still working together) remains same. If B decreases his speed by 50%, the time taken by B to complete the work becomes equal to time taken by C. Find the time taken (in hours) to complete the work if only A and C work together?

a) 4 hours

b) 5 hours

c) 6 hours

d) 8 hours

e) None of these

a

Let the time taken by A alone to complete the work = a hours, for B it is b hours, and for C, it is c hours.

1/(1/a+1/b+1/c)=8/3

From the First statement, time taken by A = half of time taken by C.

Hence, C = 2a.

From the second statement, 1.5b = c.

Hence, b = 2a/1.5

Solving these equations, a = 6hours, b= 8 hours and c= 12 hours.

Time taken by A and C working together = 1/(1/6+1/12)  = 4ho

Q.4) P, Q and R can complete a piece of work in 8, 12 and 24 days respectively. P and R started working and Q joined them after one day. If R left 2 days before complete of the work. In how many days was the work finished?

a) 17/3 days

b) 14/3 days

c) 29/6 days

d) 31/6 days

e) None of these

b

P’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/8+(x-1)/12+(x-2)/24=1

6x-4 = 24

6x = 28

X = 28/6=14/3 days.

Q.5) Three pipes P, Q and R can fill a tank in 18, 24 and 32 minutes respectively. The pipe P is closed 9 minutes 45 seconds before the tank is filled. In What time will the tank be full?

a) 18minutes

b) 16minutes

c) 14minutes

d) 12minutes

e) None of these

d

Let the tank be full in x minutes

9 minutes 45 seconds = 9.75 minutes

Therefore,

(x-9.75)/18+x/24+x/32=1

16x – 156+12x + 9x = 288

37x = 444

X=12 minutes.

Q.6) The total work is 851. Deva’s one day’s work is 17 and Bala’s one day’s work is 39. They worked for 4 days and Deva left. Maya’s one day’s work is 15. Now Maya and Bala worked for 5 days and Bala left. Diya’s one day’s work is 17. Now Diya and Maya worked for 3 days and Maya left and the rest of the work is done by Diya and Mala. If Mala’s one day’s work is 12 then how many days did Diya and Mala work?

a) 22 days

b) 25 days

c) 31 days

d) 38 days

e) None of these

e

Deva and Bala’s one day’s work is 56 and they worked for 4 days then they finished 4×56 = 224 work

Bala and Maya‘s one day’s work is 54 and they worked for 5 days then they finished 5 ×54 = 270work

Maya and Diya’s one day’s work is 32 and they worked for 3 days then they finished 3×32 = 96 work

Remaining work = 851-(224+270+96) = 261

Diya and Mala’s one day’s work is 29 and they complete the whole work in  261/29=29 days.

Q.7) A certain number of people get together to make their contribution in the construction of a Hotel. But every month three people step out of this plan. Due to this the task is completed in 1 more year instead of one year. Then how many people were originally involved in this group?

a) 79

b) 68

c) 70

d) 64

e) None of these

e

Let the total number of people = x

12x = (x+(x-3)+(x-6)+(x-9)+(x-12)+(x-15)+….(x-69))

12x = 24x – 3 (1+2+3+…23)

12x = 3×23× 24/2

X = 69

Q.8) Pipe A can fill the tank in 40 hours when it works at 30% of its efficiency. Pipe B is one-fourth as efficient as pipe A. How long will it take if both the pipes operate simultaneously at their 100% efficiency?

a) 7 hours

b) 8.1 hours

c) 9.2 hours

d) 10.4 hours

e) None of these

e

Pipe A can fill the tank when its efficiency is 100% =40× 30/100=12 hours

Pipe B can fill the tank in 48 hours.

When both the pipes operate simultaneously,

Time = (48×12)/(48+12)=9.6 hours.

Q.9) The 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 60% more efficient?

a) 75%

b) 60%

c) 50%

d) cannot be determined

e) None of these

C

Let 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 do this 80 units of work in 1 day whose efficiency is 1.6 each

So, number of new workers needed = 80/1.60=50 new workers needed.

So, percent by which workers need to be increased = 50/100×100=50%

Q.10) X and Y can complete a task in 35 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

a) 19 5/11 days

b) 60 days

c) 16 4/5 days

d) 32 days

e) None of these

c

Both X and Y can do work in 35 days.

So work done in 1 day = 1/35 th work

In 10 days, work done = 1/35×10=2/7 work

In 12 days, work done by X alone = 5/7 work

In 1 day, X can do = 5/(7×12)=5/84 th of the work

So, days X will take to complete whole work = 16 4/5  days.