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# A contractor undertakes to do a job within 100 days and hires 10 peopl

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Math Expert
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A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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09 Sep 2015, 01:11
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45% (medium)

Question Stats:

71% (02:20) correct 29% (02:38) wrong based on 622 sessions

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A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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09 Sep 2015, 10:16
7
1
12
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

CONCEPT: $$\frac{(Machine_Power * Time)}{Work} = Constant$$

i.e. $$\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}$$

In 10 workers finish 1/4 work in 20 days

Remaining work = 1-(1/4) = 3/4
No. of People left to work = 10(total) - 2(fired) = 8
Days left = ?

$$\frac{(10 * 20)}{(1/4)} = \frac{(8 * T_2)}{(3/4)}$$

i.e. $$T_2 = 75$$ Days

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Posts: 103
Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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09 Sep 2015, 03:54
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4
Solution: Let the work done by one person per day be x
Then, work done by 10 persons per day is 10x.
work done by 10 persons in 20 days is 20*10x which is equal to 1/4th of total work.
Therefore, x = 1/800.
Work done by 8 persons in n days(n*8x) is 3/4th of total work.
Therefore, n = 3/32x = 2400/32 = 75.

Option, C
##### General Discussion
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Posts: 661
Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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09 Sep 2015, 03:59
2
2
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

(10 people*20 days)/1/4=(8*x)/3/4
Solving for x, x=75
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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09 Sep 2015, 13:33
4
1
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

Total work content = 100*10 = 1000[units]

work done in 20 days by 10 people = 250[units]
20 days --- 250[units] ---10[people]
x days ---- 750[units] ---- 8[people]

x = 20*(750/250)*(10/8) = 75[days]

C
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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10 Sep 2015, 09:02
2
Step 1:

1/4 of the work was done in 20 days

So, complete work will be done in 20*4 = 80 days.

From the question stem - 10 people are hired to complete a job within 100 days - now we know they will finish this in 80 days.

Step 2:

As 20 day's work is already done, only 60 days of work remains. We know that 2 people have been fired, so we can use unitary method to solve the number of days required:

People working --------- days required to complete 3/4 of the work

10 -------------------------- 60
1 ----------------------------- 60/10
8 ------------------------------------ 60*8/10 = 75

Option C
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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10 Sep 2015, 09:15
2
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

Work done by 10 people in 10 days = 1/4
Work to be completed by 8 people = 3/4
Let x be the time taken by 8 people to complete 3/4 work.
Then, at constant rate R
$$\frac{M_1RT_1}{W1}$$ = $$\frac{M_2RT_2}{W2}$$

or $$\frac{20*10*R}{\frac{1}{4}} = \frac{x*8*R}{\frac{3}{4}}$$

or x= 75
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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13 Sep 2015, 07:29
1
2
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Can we say that 10 people can finish the work in 100 days? No. If that were the case, after 20 days, only 1/5th of the work would have been over. But actually 1/4th of the work is over. This means that ‘10 people can complete the work in 100 days’ was just the contractor’s estimate (which turned out to be incorrect). Actually 10 people can do 1/4th of the work in 20 days. The contractor fires 2 people. So the question is how many days are needed to complete 3/4th of the work if 8 people are working?

We need to find the number of days. How is ‘no. of days’ related to ‘no. of people’ and ‘work done’?

If we have more ‘no. of days’ available, we need fewer people. So ‘no. of days’ varies inversely with ‘no. of people’.

If we have more ‘no. of days’ available, ‘work done’ will be more too. So ‘no. of days’ varies directly with ‘work done’.

Therefore,
‘no. of days’ * ‘no. of people’/’work done’ = constant

$$20*\frac{10}{(\frac{1}{4})} =$$ ‘no. of days’*$$\frac{8}{(\frac{3}{4})}$$

No. of days = 75

So, the work will get done in 75 days if 8 people are working.

We can also do this question using simpler logic. The concept used is joint variation only. Just the thought process is simpler.

10 people can do 1/4th of the work in 20 days.

8 people can do 3/4th of the work in x days.

Start with the no. of days since you want to find the no of days:

$$x = 20*(\frac{10}{8})*(\frac{3}{1}) = 75$$

From where do we get 10/8? No. of people decreases from 10 to 8. If no. of people is lower, the no of days taken to do the work will be more. So 20 (the initial no. of days) is multiplied by 10/8, a number greater than 1, to increase the number of days.

From where do we get (3/1)? Amount of work increases from 1/4 to 3/4. If more work has to be done, no. of days required will be more. So we further multiply by (3/4)/(1/4) i.e. 3/1, a number greater than 1 to further increase the number of days.

This gives us the expression $$20*(\frac{10}{8})*(\frac{3}{1})$$

We get that the work will be complete in another 75 days.

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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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12 Feb 2016, 18:58
1
We can also use the concept of man-days here

100 days -->10men so the job includes 100*10=1000 man-days

After 20 days

1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done

Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8

Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)

Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75

Ans: C (75 days)
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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12 Feb 2016, 19:16
3
1
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

Hi,
Just a POINT on wordings..
It would have been better, if it mentioned that all worked with same and constant speed

A quick approach could be..
so we assume that all have same capabilities to work..

1/4 work done in 20 days..
so remaining work can be done in 60 days with 10 person..
in the same ratio, the work can be done by 1 person in 60*10 days=600..
and 8 will do it in= 600/8= 75 days

C
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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13 Feb 2016, 06:27
2
1
Rate = Work/ Time

10 person team:
Work = 1/4 total
Time = 20 days
Rate = (1/4)/ 20 days = 1/4 *1/20 = 1/80

Rate of 1 person --> 1/80 * 1/10 = 1/800

8 person team:
Work = 3/4 total
Rate = 1/ 800 * 8 = 1/100
Time = (3/4) / (1/100) = 3/4 *100 = 75 days
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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08 Jul 2017, 08:29
1
Estimated rate by contractor is 1/1000 (10 workers *100 days)
As per this rate,the amount of work completed after 20 days should have been 20% which is not the case as 25 % work was done after 20 days by 10 workers
Thus the actual rate of workers would be 1/x*10*20=1/4————1/x=1/800
At the rate of 1/800, 8 workers would require 'y' days to complete the rest of the 75% work
1/800*8*y=3/4
y=3/4*800/8
y=75
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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14 Aug 2017, 08:52
My solution
Let’s assume that each of the men’s performance is 1 piece of work
Then (1*10) * 100 = 1000 should be produced in 100 days by 10 men
during 20 days they did a quarter of required 1000 so it’s 250
(1.25 * 10) *20 = 250
He fires 8 and the remaining work is 750
Then
(1.25*8)*x=750 solve for x = 75
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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18 Aug 2017, 07:58
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

The rate of 10 people is (1/4)/20 = 1/80.

After firing 2 people, 8 people are left. We can use the following proportion to determine the rate of 8 people:

10/(1/80) = 8/x

800 = 8/x

800x = 8

x = 1/100

Thus, it will take (3/4)/(1/100) = 300/4 = 75 days more to complete the job.

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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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18 Sep 2017, 22:21
1
In 20 days, 10 employees have done 1/4 of the entire job.

That means the daily rate of 1 employee is: 1/(40*20) = 1/800

Now it is stated that 2 were fired, which leaves us with 8 guys to the 3/4 of the initial job and we want to know in how many days they'll be able to do it. Let "x" be that number of days:

$$(1/800) * 8x = 3/4$$

$$x = (3*100)/4$$
$$= 75 days.$$
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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25 Sep 2017, 01:04
let the total amount of work to be done be X
Then, 20*10=1/4X
X=800
and 25% of the work is done in 20 days which means 200 unit of work is completed by 10 men in 20 days
and the rest 600 unit of work is to be done by 8 men
Therefore,600/8= 75

Kudos if you find this explanation helpful
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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21 Oct 2017, 09:37
GMATinsight wrote:
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

CONCEPT: $$\frac{(Machine_Power * Time)}{Work} = Constant$$

i.e. $$\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}$$

In 10 workers finish 1/4 work in 20 days

Remaining work = 1-(1/4) = 3/4
No. of People left to work = 10(total) - 2(fired) = 8
Days left = ?

$$\frac{(10 * 20)}{(1/4)} = \frac{(8 * T_2)}{(3/4)}$$

i.e. $$T_2 = 75$$ Days

Hi
could you explain the concept, please?
unfortunately, I haven't seen it yet
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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21 Oct 2017, 09:48
1
soodia wrote:
GMATinsight wrote:
Bunuel wrote:
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Kudos for a correct solution.

CONCEPT: $$\frac{(Machine_Power * Time)}{Work} = Constant$$

i.e. $$\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}$$

In 10 workers finish 1/4 work in 20 days

Remaining work = 1-(1/4) = 3/4
No. of People left to work = 10(total) - 2(fired) = 8
Days left = ?

$$\frac{(10 * 20)}{(1/4)} = \frac{(8 * T_2)}{(3/4)}$$

i.e. $$T_2 = 75$$ Days

Hi
could you explain the concept, please?
unfortunately, I haven't seen it yet

Hi soodia,

the formula can be derived by applying unitary method

$$10$$ people completed $$\frac{1}{4}$$th work in $$20$$ days

so $$1$$ people will complete whole i.e $$1$$ work in $$20*10*4$$ (no of days will increase as only $$1$$ person is working)

Hence $$8$$ people will complete the remaining $$\frac{3}{4}$$th work in $$\frac{20*10*4*3}{8*4} = 75$$ days
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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10 Nov 2017, 13:11
lenric wrote:
In 20 days, 10 employees have done 1/4 of the entire job.

That means the daily rate of 1 employee is: 1/(40*20) = 1/800

Now it is stated that 2 were fired, which leaves us with 8 guys to the 3/4 of the initial job and we want to know in how many days they'll be able to do it. Let "x" be that number of days:

$$(1/800) * 8x = 3/4$$

$$x = (3*100)/4$$
$$= 75 days.$$

By far the quickest method. Nice one.
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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl  [#permalink]

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24 Aug 2018, 21:14
2
The approach below is detailed for the understanding purposes, however once you know the logic behind it, you'd be able to solve the question faster.

Consider giving Kudos if it helps :D

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Re: A contractor undertakes to do a job within 100 days and hires 10 peopl   [#permalink] 24 Aug 2018, 21:14

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