Basic Time & Work problems

Question

Hi,

I was hoping to get the correct approach for the following types of basic problems in Time & Work.

Type I - Extra number of men required/employed

1) An engineer undertakes a project to build a road 15 km long in 300 days with 45 men employed. After 100 days, only 2.5 km of the road has been completed. Find the (approx.) number of extra men needed to complete the work in time.

a) 43
b) 45
c) 55
d) 68
e) 60

OA -  D

Type II - when amount paid is included

1) A can do a piece of work in 12 days. A and B complete the work together and were paid Rs. 54 and Rs. 81 respectively. How many days must they have taken to complete the work together?

a) 4 days
b) 4.5 days
c) 4.8 days
d) 5 days
e) 4.2 days

OA -  C

Type 3 - men leave halfway through work

1) In a fort, there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?

a) 12 days 
b) 10 days
c) 8 days
d) 6 days

OA -  D

Any pointers would be helpful.

ezhilkumarank · Answer

Type 3 - men leave halfway through work

1) In a fort, there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?

a) 12 days 
b) 10 days
c) 8 days
d) 6 days

Food Availability 
    Men  Days  Quantity  
  Given  200  31  6200  
  Till 27 days  200  27  5400  
  From 28th day  80  x  800

Hence the number of days the remaining quantity will last = 10 days. However the original quantity was to last for only 4 more days if none of the soldiers had left.

Hence extra days is 10-4 = 6 days (D).

ezhilkumarank · Answer

Type II - when amount paid is included

1) A can do a piece of work in 12 days. A and B complete the work together and were paid Rs. 54 and Rs. 81 respectively. How many days must they have taken to complete the work together?

a) 4 days
b) 4.5 days
c) 4.8 days
d) 5 days
e) 4.2 days

Given A can do the work in 12 days. Hence A's rate is 1/12.

Also amount payment made to A and B is Rs 54 and Rs 81 respectively -- which is the ratio of 2:3.

Viewing only A's data: Since payment is proportional to the amount of work done.

Fraction of the total work done by A * Days in which A would have completed the work alone.

Hence (2/5) * 12 = 4.8 days. Hence A worked for 4.8 days @ a rate of (1/12) along with B to complete the work.

Answer C (4.8).

KarishmaB · Answer

Type I:

To complete 2.5 km in 100 days, we need 45 men
To complete 12.5 km (leftover road) in 100 days, we need 45 x 12.5/2.5 men (It will be 12.5/2.5 and not 2.5/12.5 because more work will need more men. So we have to make 45 greater. Direct variation.) = 225 men

To complete 12.5 km in 100 days we need 225 men.
To complete 12.5 km in 200 days (this is the number of leftover days), we need 225 x 100/200 (Now if we have more days for same work, we need less men so 100/200 to make 225 smaller. Inverse Variation) = 112.5 men i.e. 113 men (112 men cannot finish the work. Even if this was 112.3, I would have made it 113)

We already have 45 men, we need 68 more.

Note: I could have done the above in a single step by saying 45 x 12.5/2.5 x 100/200 = 112.5
I used two steps to clarify.

Type II:
If we are given how much they were paid, we know the ratio of their rate of work. It will be the ratio in which they were paid. This is so because if you are twice as fast as me, you will be paid twice as much as me.
Ratio of rate of work = 54:81 = 2:3
Then, ratio of time taken will be 3:2 (Ratio of rate of work is inverse of ratio of time taken. If this is unclear, just check out work theory)
Then, B can do the work in 8 days.
Together, they will take 8 x 12/ (8 + 12) = 4.8 days

Type III:
Let me say that the amount of food one soldier consumes in one day is 1 soldier-day food.

Total amount of food was 200 x 31 soldier-days = 6200 soldier-days 
In 27 days, 200 soldiers consumed the food which is equal to 27 x 200 = 5400 soldier-days.
Left over food = 800 soldier-days
Now 800 soldier-days food will last 80 soldiers 10 days. Since 27 days are already over, it would have lasted only 4 more days but now it is going to last 10 days so it will last an extra 6 days.

ezhilkumarank · Answer

Type I - Extra number of men required/employed

1) An engineer undertakes a project to build a road 15 km long in 300 days with 45 men employed. After 100 days, only 2.5 km of the road has been completed. Find the (approx.) number of extra men needed to complete the work in time.

a) 43
b) 45
c) 55
d) 68
e) 60

Answer:

Work and Rate 
    Rate  Men  Days  Work completed in meters  
  First 100 days  x  45  100  2.5*1000

We can find out the actual rate (x) at which the men are working.
=> x*45*100 = 2500
=> x = 5/9.

Now we will use the actual rate at which the men are working to find out the extra men required to complete the work in the remaining 200 days.

Work and Rate 
    Rate  Men  Days  Work completed in meters  
  First 100 days  5/9  45  100  2.5*1000  
  Next 100 days  5/9  x  200  12.5*1000

(5/9)*x*200 = 12500
=> x = 112.5 ~ 113. So the number of extra men required to complete the work in the remaining 200 days is 113 - 45 = 68.

Answer

nehab2011 · Answer

Great! Thank you for the help ezhilkumarank and VeritasPrepKarishma. For Time & Work, i tend to directly solve problems using the one days work approach. And for the above problems that approach did not get me the right answer.
Thank you for the help!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Basic Time & Work problems

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Food Availability
	Men	Days	Quantity
Given	200	31	6200
Till 27 days	200	27	5400
From 28th day	80	x	800

Work and Rate
	Rate	Men	Days	Work completed in meters
First 100 days	x	45	100	2.5*1000