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23 Oct 2010, 09:42
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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 -
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 -
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 -
Any pointers would be helpful.
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 -
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 -
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 -
Any pointers would be helpful.
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Updated on: 23 Oct 2010, 17:57
Originally posted by ezhilkumarank on 23 Oct 2010, 17:44.
Last edited by ezhilkumarank on 23 Oct 2010, 17:57, edited 1 time in total.
Last edited by ezhilkumarank on 23 Oct 2010, 17:57, edited 1 time in total.
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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
[/quote]
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).
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).
23 Oct 2010, 17:56
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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).
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).
23 Oct 2010, 18:13
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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.
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.
