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

(10 people*20 days)/1/4=(8*x)/3/4
Solving for x, x=75
Answer C

Answer is C.

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

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

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
Answer:- C

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.

Answer (C)

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)

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

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

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

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.

Answer: C

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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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


A,D,E are out for obvious reasons. Now, we are left with B and C. If contractor doesn't fire any worker, then it will take them 60 days, but since he is firing 2 workers (or 20%), the work will be slowed down by 20% as well. So 60 days is 80%, 75 days is 100%

Rate * Time = Work done => r * t =w

=> \(\frac{(r * t) }{ w}\) = constant

10 people work for 20 days to complete \((\frac{1}{4})^{th}\) work:\(\frac{10 * 20}{\frac{1}{4}}\)

10-2 = 8 people work for 't' days to complete \((\frac{3}{4})^{th}\) work:\(\frac{8 * t}{\frac{3}{4}}\)


=> \(\frac{10 * 20}{\frac{1}{4}}\) = \(\frac{8 * t}{\frac{3}{4}}\)

=> 10 * 20 * 4 = \(\frac{(8 * t * 4) }{ 3}\)

=> 25 * 3 = t

=> 75

Answer C

Let the job = the product of the blue values above = 10*20*4 = 800 widgets.
Since 1/4 of the 800 widgets -- in other words, 200 widgets -- are produced in 20 days, the combined rate for 10 workers \(= \frac{work}{time} = \frac{200}{20} = 10\) widgets per day.
Since 10 workers produce 10 widgets per day, the rate per worker = 1 widget per day.

Since the rate per worker = 1 widget per day, the daily rate for 8 workers after 2 workers are fired = 8 widgets per day.
Time to produce the remaining 600 widgets at a rate of 8 widgets per day \(= \frac{work}{rate} = \frac{600}{8}\) = 75 days.

Played with numbers.
100 x 10 x 1/4 = 250
(250/20)/10 = 12.5
12.5 x 0.75 x 8 =75

­


For this question, table method may be little confusing under time pressure.

Lets solve with simple logic...

Initially 10 men would work for 20 days. 

so total unit of works done in 20 days = 20*10=200 units .

Now 200 units of work is 1/4th of the total work. Assume the total units of works be x. 

So, 1/4*X = 200 , X= 800( Total units of works)

So remaining work to be done is 800-200=600 units.

2 men are fired, 8 men remain to finish the 600 units of work. 

So time require to finish the work is 600/8 =75 days. 

Option C. 


Hope this helps.