Time and Work

# Time and Work

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A works twice as fast as B. If B can complete a work in 18 days independently, the number of days in which A and B can together finish the work in:

(a.) 2 days

(b.) 6 days

(c.) 4 days

(d.) 5 days

(e.) None of thes

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Well done Vidisha, continue to ask questions

Let total work = 120 unit

And the work completed after n days.

1st day work =1 unit

2n day work = 2 unit

3rd day work = 3 unit

………………..

………………..

nth day work = n unit

1 + 2 + 3+ 4 + …………….+n =120

n (n+1)/2 = 120

n2 + n = 240

n2 + n – 240 = 0

n2 + 16n -15n – 240 =0

n(n+ 16) – 15(n + 16) = 0

(n-15)(n+ 16) = 0

n = 15 or n =-16

Required days = 15

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Hello Tina,

Let total work is 18 unit.

B can complete 1 unit work in 1 day.

So, A can complete 2 unit work in 1 day.

One day work of A and B = 1 + 2 = 3 unit.

Required days to complete 18 unit by A and B both = 18/3 = 6 days.

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Hello sir,

Please solved this question. This question was asked in Cat 2017 in slot- 1

A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, every day a new person with the same efficiency joins the work. How many days are required to complete the job?

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The efficiency of man is reduced by half every two hours.He could have completed the work in 150 hours at maximum efficiency.How many hours does he take if his efficiency becomes maximum after every 8 hours and then reduces as mentioned above?

0

Hello Vidisha,

At maximum efficiency, he finishes the work in 150 hrs that means the amount of work done in 2 hrs at maximum efficiency = 1/75.

For next two hours he finishes = 1/150 amount of work.

In next two hours he does = 1/300 amount of work and

in another two hours, he finishes = 1/600 amount of work.

That means in total 8 hrs he does = (1/75)(1 + 0.5 + 0.25 + 0.125) = 1.875/75 = 1/40 amount of work.

As he regains his maximum efficiency after every 8 hrs, he does the same amount of work in every 8 hrs span.

So total time required to complete the work = 8*40 = 320 hrs.

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A worker working under a bonus scheme saves 10 hours in a job for which the standard time is 60 hrs. A bonus of 10% of the hourly rate is payable when he reaches 100% efficiency. An additional bonus of 2% of the hourly rate for each 1% in excess of 100% efficiency is given. If the normal wage rate is Rs.2 per hour, find the wages payable to the worker.

0

A mother along with her two sons is entrusted with the task of cooking biryani for a family get together. It takes 30 minutes for all three of them cooking together to complete 50 percent of the task. The cooking can also be completed if the two sons start cooking together and the elder son leaves after 1 hour and the younger son cooks for further 3 hours. If the mother needs 1 hour less than the elder son to complete the cooking, how much cooking does the mother complete in an hour?

a. 33.33%

b. 50%

c. 66.67%

d. none of these

0

Let the time in which tank will be  filled is  x minutes
So,

x/60 + ( x -10)/30 + ( x-20)/20 = 1

on solving x = 70/3 i.e 23 minutes 20 seconds

Hence , option 2.

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The efficiency of a man is reduced by half every two hours . At maximum efficiency, he could have completed the job in 150 hours . How how many hours does it take him to complete it the job , if his efficiency becomes maximum after every 8 hours and then reduces as mentioned above?

37 whole 11/17 answer hai ?

let efficiency be 16

total work = 16*150= n(2*16 +2*8 +2*4 +2*2)

n= (16*150)/2*30 =40

let the work be 150 units

and his maximum efficiency be 1 unit per hour so work done in 8 hours = 2( 1 + 1/2 + 1/4 + 1/8) = 15/4 units

Hence total time taken : 150/ ( 15/4) = 40 slots of 8 hour each

Total : 320 hours.

0

12 men or 18 women can dig a cylindrical well of radius 2.4 meters and height 6 meters in 9 hours. In how many hours 6 men and 11 women can dig a cylindrical well of radius 3.6 meters and height 8 meters?

24.3?

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Pipe A and pipe B can alone fill the tank respectively in 18 hours and 24 hours. A third pipe C empty the tank in 36 hours. If pipe A open at 8:00 am, pipe B open at 10:00 am and pipe C open at 1:00 pm. At what time tank will be full fill?

11:36?

let total work be 144 then efficiency of A= 144/18=8

B=144/24=6

C=144/36=-4 (negative because it empties tank )

since A works from 8 to 1 means he work for 5 hours and and B works from 10 to 1 means for 3 hours and then C starts with A and B

5*8 + 6*3 + (8+6-4)t= 144

t=8 hours 36 min

0

A and B together can do a piece of work in 7 days. If A does twice as much work as vinay in a givem timw,  how long will arun alonw take to do the work?

Let’s assume

Time taken by A to do the work : x days
so time taken by B: 2x days

work done by A in 1 day : 1/x units
Work done by B in 1 day : 1/2x units

Work done by A and B in 1 day = 1/7 units

So, 1/x + 1/2x = 1/7

Solving this we get x = 21/2

So A alone  takes 21/2 days .

0

Raju can do a work in 10 days,  vicky in 12 days and tinku in 15 days.  They all started the work together,  but raju leaves after 2 days and vicky leaves 3 days before the work is completed. In how many days is the work completed?

Total work : 60 units [ LCM of 10,12 and 15]

Raju can do the work in 10 days so he does 60/10 = 6 units / day

similarly Vicky does 5 units/ day and

Tinku does 4 units per day

Raju left the work after 2 days so work done by Raju , Vicky and Tinku in first two days = ( 6 + 5 + 4) x 2 = 30 units

Vicky  left the work 3 days before its completion , so Tinku alone does : 4 x 3 = 12 units

So remaining ( 60 - 30 - 12) = 18 units  work was done by Vicky and Tinku so 18/ ( 4+5) = 2 days

So total days : 2 + 2 + 3 = 7 days.

0

A and B can do a job in 10 days working together whereas B and C can finish the same job in 15 days working together. If A works for 5 days and B works for 8 days and C takes 9 days to finish the job. How much time will C take to finish the complete
job alone?

A. 8
В. 12
C. 18
D 20

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