CRE 4 - Man Days (single group of people) | Time and Work
If 10 men can do a piece of work in 8 days, in how many days can 8 men do the same work?
Answer: 10
Explanation :
Total work = Men × Days
Since total work is same in both cases.
⇒ Work done by 10 men in 8 days = Work done by 8 men in 10 days.
∴ M1 × D1 = M2 × D2
⇒ 10 × 8 = 8 × x
⇒ x = (10 × 8)/8 = 10 days.
Hence, 10.
Workspace:
15 men can do a piece of work in 56 days. How many men are needed to do the work in 7 days?
- A.
60
- B.
120
- C.
150
- D.
145
- E.
180
Answer: Option B
Explanation :
15 men can do a piece of work in 56 days.
∴ M1 = 15, D1 = 56 days
Let x be the number of men needed to do the same work in 7 days.
∴ M2 = x, D2 = 7 days
∵ Work done by 15 men in 56 days = Work done by x men in 7 days
∴ M1 × D1 = M2 × D2
∴ 15 × 56 = x × 7
∴ x = 120 men
Hence option (b).
Workspace:
If 4 men can reap 80 hectares in 48 days, then how many hectares can 24 men reap in 30 days?
Answer: 300
Explanation :
When M1 men can complete W1 work in D1 days while M2 men can complete W2 work in D2 days, then
∴ =
Now, 4 men can reap 80 hectares in 48 days, and 24 men reap 'x' hectares in 30 days.
⇒ =
⇒ =
⇒ x = 300
Hence, 300.
Workspace:
If 8 men can cut a number of trees in 24 days by working 6 hours a day, for how many hours a day would 3 men have to work in order to cut thrice the number of trees in 48 days?
- A.
24 hours
- B.
20 hours
- C.
16 hours
- D.
18 hours
- E.
22 hours
Answer: Option A
Explanation :
Let 8 men can cut 'x' number of trees in 24 days working 6 hours a day, while 3 men can cut '3x' number of trees in 48 days working 'h' hours per day.
∴ =
⇒ =
⇒ h = = 24
Hence, 24.
Workspace:
18 men can make 168 wood chairs in 10 hours. If 3 men leave the job how many chairs will be made in 8 hours?
- A.
144
- B.
132
- C.
120
- D.
112
- E.
96
Answer: Option D
Explanation :
18 men in 10 hours make 168 wood chairs i.e. work done by 18 men in 10 hours is 168.
After 3 men leave, total number of men = 18 – 3 = 15
Let 15 men make x chairs in 8 hours.
∴
∴ x = 112 chairs
Hence, option (d).
Workspace:
A certain number of men can finish a piece of work in 20 days. If however there were 10 men less it will take 20 days more for the work to be finished. How many men were there originally?
- A.
25
- B.
13
- C.
15
- D.
20
- E.
None of these
Answer: Option D
Explanation :
Let the number of men initially be 'm'.
m men can complete the work in 20 days while (m - 10) men can complete the same work in 40 days.
∴ m × 20 = (m - 10) × 40
⇒ m = 2m - 20
⇒ m = 20
Hence, option (d)
Workspace:
If 90 women working 9 hours a day can do a piece of work in 18 days, in how many days will 54 women working 6 hours a day do the same work?
- A.
15 days
- B.
24 days
- C.
30 days
- D.
36 days
- E.
45 days
Answer: Option E
Explanation :
Work rate = 90 women
Time = (18 × 9) hours
∴ Work done = (90 × 18 × 9) women hours
Later, work rate = 54 women
Time = (d × 6) hours (d = number of days)
Since work done is the same,
∴ 90 × 9 × 18 = 54 × 6 × d
d = 45 days
Hence, option (e).
Workspace:
In a hospital there is sufficient food for its 900 patients for 60 days. After 40 days, 400 patients are discharged from the hospital and no new ones are added. For how many extra days will the rest of the food last for the remaining patients if each patient consumed the same amount of food?
- A.
14 days
- B.
2 days
- C.
12 days
- D.
16 days
- E.
6 days
Answer: Option D
Explanation :
Total food available for 900 patients for 60 days = 900 × 60 units
Total food consumed by 900 patients in 40 days = 900 × 40 units
Food remaining = 900 × 20 units
Number of patients remaining = 500
∴ Number of days = 18000/500 = 36
∴ Number of extra days = 36 – 20 = 16 days
Hence, option (d).
Video Solution:
Workspace:
112 boys manufacture 128 toys in a day by working 8 hours; in how many days can 42 boys manufacture 210 toys by working 5 hours a day?
- A.
2
- B.
4
- C.
7
- D.
10
- E.
14
Answer: Option C
Explanation :
112 boys manufacture 128 toys in a day by working 8 hours
Let 42 boys manufacture 210 toys by working 5 hours a day, in x days
∴ =
∴ 112 × 1 × 8 × 210 = 42 × x × 5 × 128
∴ x = 7 days
Hence, option (c).
Workspace:
Running at the same constant rate, 6 identical machines can produce a total of 180 bottles per hour. How many bottles could 15 such machines produce in 30 minutes?
- A.
225
- B.
300
- C.
250
- D.
350
Answer: Option A
Explanation :
6 machines can produce 180 bottles per hour
Hence, 1 machine can produce 180/6 = 30 bottles per hour and 15 bottles in 30 minutes.
∴ 15 machines can produce 15 × 15 = 225 bottles per hour.
Alternately,
=
⇒ =
⇒ B = = 225
Hence, option (a).
Workspace:
If 10 men can dig a well in 7 days by working 12 hours a day. What is the number of men required to dig a well in 4 days by working 14 hours a day?
- A.
15
- B.
10
- C.
12
- D.
8
- E.
6
Answer: Option A
Explanation :
10 men working 6 hours a day can dig a well in 7 days.
Let x be required to dig a well in 4 days by working 14 hours a day.
∴ 10 × 7 × 12 = x × 4 × 14
∴ x = 15 men
Hence, option (a).
Workspace:
During a severe draught, a society of 280 members had sufficient water stored for 180 days. After 100 days 40 new members joined the society. For how many days after the 40 new members joined the society would the rest of the water be sufficient assuming everyone consumed the same amount of water?
- A.
44 days
- B.
50 days
- C.
56 days
- D.
64 days
- E.
70 days
Answer: Option E
Explanation :
Total water available for 280 members for 180 days = 280 × 180 units
Total available consumed by 280 members in 100 days = 280 × 100 units
Water available after 100 days = 280(180 – 100) = 280 × 80 units
Number of members after 100 days = 320
∴ Number of days that the water will sufficient = 22400/320 = 70 days.
Hence, option (e).
Video Solution:
Workspace:
If 16 men, working for 4 hrs per day for 8 days get 80/- then how many men required if the work is 6 hrs per day for 16 days they get 120/-?
- A.
9
- B.
7
- C.
6
- D.
8
- E.
10
Answer: Option D
Explanation :
Let the men required = x
We know that
Work = strength × time
∴
∵ Work ∝ wages
∴
⇒ x = 8 men
Hence, option (d).
Video Solution:
Workspace:
If 400 soldiers eat 20 tonnes of food in 100 days, how much will 40 soldiers eat in 20 days?
- A.
1 ton
- B.
10 kg
- C.
100 kg
- D.
200 kg
Answer: Option D
Explanation :
The amount of food consumed by 400 soldiers in 100 days = 10 tonnes = 10 × 1000 = 10000 kg
The amount of food consumed by 400 soldiers in 20 days = (20 × 10000)/100 = 2000 kg
The amount of food consumed by 40 soldiers in 20 days = 2000/10 = 200 kg
Hence, option (d).
Video Solution:
Workspace:
Feedback
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.