John appointed 25 men to complete a small bridge in 40 days after 20

Question

John appointed 25 men to complete a small bridge in 40 days. After 20 days he appointed 15 more workers and the bridge was completed 5 days earlier. If he had not appointed the additional workers by how many days he would have been behind the schedule time ?

A)2 days
B)3 days
C)4 days
D)5 days
E)5/2 Days

A) 2 days
B) 3 days
C) 4 days
D) 5 days 
E) 5/2 Days

KarishmaB · Accepted Answer

25 men worked for 20 days and did 25*20 = 500 units of work
40 men worked for 15 days (the bridge was needed to be completed in 40 days but got done 5 days earlier) and did 40*15 = 600 units of work

So total work was 1100 units of work.
Had 25 men been there for the entire time, time taken = 1100/25 = 44 days

So he would have been 4 days behind the scheduled time.

Answer (C)

gracie · Answer

25 men*20 days=500 total man days for original crew
40 men*15 days=600 total man days for enhanced crew
500/(500+600)=5/11 of job completed by original crew 
let r=daily rate of original crew
r*20=5/11
r=1/44
44-40=4 days behind
C

pushpitkc · Answer

Given:   Originally, the work was to be completed by 25 workers in 40 days. If we assume the total
work a worker does in a day to be 1 units, the total work must be 1000(40*25) units.

In second statement of question stem we are given "After 20 days he appointed 15 more workers
and the bridge was completed 5 days earlier" - Here, we need to know how many workers actually
did the job.

x workers work for 20 days and x+15 work for 15 days to complete the work in 35 days. 
 x*20+ (x+15)15 > 1000  ->  35x > 775  ->  x > 22 . Minimum workers must be 23

Now, 23 workers complete 23*40 units or 920 units of work in 40 days. 
Incomplete work: 80 units | Therefore, it will take 4(Option C) days in order to complete the pending work.

Mizan383838 · Answer

Suppose, 1 man's 1 days' work = x

Now, 25*x*20+ 40*x*15 = 1
=>x = 1/1100

Again, 
suppose, y days needed to complete whole work

Now,

25*y/1100=1

=> y = 44

So, extra days= 4 (ans)

Posted from my mobile device

Kinshook · Answer

Given: John appointed 25 men to complete a small bridge in 40 days. After 20 days he appointed 15 more workers and the bridge was completed 5 days earlier.

Asked: If he had not appointed the additional workers by how many days he would have been behind the schedule time ?

Total man-days required to complete the small bridge = 25*20 + (25+15)*(40-5-20) = 25*20 + 40*15 = 500 + 600 = 1100 man-days
Days required by 25 men to complete the bridge = 1100/25 = 44 days

If he had not appointed the additional workers, he would have been behind the schedule by days = 44-40 = 4 days

IMO C

01862603526 · Answer

Firt part. 25 men take 20 days.
Second part. 25+15=40 take 15 days, so 1 man take= 40×15
So 25 men take =40×15÷25=24 days.so 25 men take to complete the bridge in 20+24=44 days. He would have been behind scheduled time by 4 days.

Posted from my mobile device

anirudhjay · Answer

Shouldn't it be explicit that the additional workers work at the same capacity or work per unit time as the other 25 men? I had to figure out the implicit assumption, since the problem would otherwise be unsolvable.

Bunuel · Answer

A properly written GMAT question would state that explicitly. In this problem, as you correctly noted, if you do not assume that all workers work at the same rate, the question is unsolvable. So here you should simply make that assumption and proceed.

patpathaha · Answer

1 men : 1 day : 1/x bridge done
=> 25 men : 1 day : 25/x bridge done
=> 25 men : 20 days : 25*20/x = 500/x bridge done
so after the first 20 days, 500/x bridge is done

1 men : 1 day : 1/x bridge done
he add 15 men to the existing 25 men, so now we have 40 men => 40 men : 1 day : 40/x bridge done
the deadline is 40 days, 20 days have passed, and they complete 5 days earlier, so the rest of the time all 40 men works is 40-20-5=15 days => 40 men : 15 days : 40*15/x = 600/x bridge done

After 35 days, 1 bridge should be completely done
=> 500/x + 600/x = 1 => x = 1100

=> 1 men : 1 day : 1/1100 bridge done
=> 25 men : 1 day : 25/1100 = 1/44 bridge done
=> 25 men :  44 days  : 1/44*44 = 1 bridge done
=> they need 44 days

John appointed 25 men to complete a small bridge in 40 days after 20

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John appointed 25 men to complete a small bridge in 40 days after 20

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