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- Question
- A, B and C can do a piece of work in 16, 32 and 48 days, respectively. They all begin together. A work continuously till it is finished, C leaves the work 2 days before its completion and B leaves the work in 1 days before its complete. In what time is the work finished?
Options- A. 10 days
- B. 20 days
- C. 15 days
- D. 30 days
- Correct Answer
-
ExplanationLet the work be finished in N days.
Then, A's N day's work + B's (N - 1) days + work + C's (N - 2) day's work = 1
? N/16 + (N - 1/32) + (N - 2/48) = 1
? N/1 + N - 1/2 + N - 2/3 = 16
? (6N + 3N - 3 + 2N - 4)/6 = 16
? 11N - 7 = 96
? 11N = 103
? N = 103/11 = 94/11 days - 1. A contract is to be complete in 92 days and 234 men were set to work, each working 16 h a days. After 66 days, 4/7 of the work is completed. How many addition men may be employed, so that the work may be completed in time, each man now working 18 h a day?
Options- A. 162
- B. 234
- C. 262
- D. 81 Discuss
- 2. A contractor undertook to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharge now, so that the work finish in time?
Options- A. 40
- B. 50
- C. 48
- D. 56 Discuss
- 3. 3 women and 18 children together take 2 days to complete a piece of work. How many days will 9 children alone take to complete the piece of work, if 6 women alone can complete the piece of work in 3 days?
Options- A. 9
- B. 7
- C. 5
- D. 6 Discuss
- 4. In a factory, there are equal number of women and children. Women work for 6 h a days and children for 4 h a day. During festival time, the work load goes up by 50%. The government rule does not allow children to work for more then 6 h a day. If they are equally efficient and the extra work is done by women, then extra hours of work put in by women everyday are?
Options- A. 5
- B. 3
- C. 4
- D. 9 Discuss
- 5. If 14 men and 12 boys can finish work in 4 days, while 8 men and 16 boys can finish the same work in 5 days. Compare the 1 days work of 1 man and 1 boy.
Options- A. 2
- B. 11/2
- C. 1/2
- D. 3 Discuss
- 6. Rashmi can do a piece of work in 16 days. Ravina can do the same work in 12 4/ 5 days, while Gitika can do it in 32 days. All of them started to work together but Rashmi leaves after 4 days. Ravina leaves the job 3 days before the completion of the work. How long would the work last?
Options- A. 9 days
- B. 6 days
- C. 18 days
- D. 5 days Discuss
- 7. Pipe A can fill a tank in 45 hrs and pipe B can fill it in 36 hrs. If both the pipes are opened in the empty tank. In how many hours will it be full?
Options- A. 10 hr
- B. 15 hr
- C. 20 hr
- D. 28 hr Discuss
- 8. If a pipe fills a tank in 6 h, then what part of the tank will the pipe fill in 1 h?
Options- A. 1/3
- B. 1/6
- C. 1/4
- D. 1/5 Discuss
- 9. A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options- A. 16 hrs.
- B. 20 hrs.
- C. 25 hrs.
- D. 40 hrs. Discuss
- 10. A pipe can empty a tank in 12 minutes and another pipe can empty it in 16 minutes. If both the pipes are opened simultaneously, find the time in which a full tank is emptied?
Options- A. 6 minutes
- B. 61/7 minutes
- C. 62/7 minutes
- D. None of these Discuss
Time and Work problems
Search Results
Correct Answer: 162
Explanation:
Remaining work = 1 - (4/7) = 3/7
Remaining period = (92 - 66) = 26 days
Let the number of addition men = N
Given, M1 = 234, D1 = 66, T1 = 16, W1= 4/7,
M2 = (234 + x), D2 = 26, T2 = 18, W2 = 3/7
According to the question,
M1W2T1D1= M2W1T2D2
? 234 x (3/7) x 16 x 66 = (234 x N) x (4/7) x 18 x 26
? 234 + N = (3 x 66 x 16 x 234) / (4 x 26 x 18)
? 234 + N = 36 x 11 = 396
? N = 396 - 234 = 162
Additional men to be employed = 162
Correct Answer: 56
Explanation:
Given, M1 = 120, M2 = 120 - n, D1 = 64, D2 = 60
W1= 2/3 and W2 = 1/3
According to the formula,
(M1D1) / W1 = (M2D2) / W2
? [120 x (64/2)] / 3 = [(120 - n) x 60] / (1/3)
? (120 x 64) / (2 x 60) = (120 - n)
? (120 - n) = 64
? n = 120 - 64 = 56
Now, 56 men can be discharged to finish the work in time.
Correct Answer: 6
Explanation:
Since, 3 women + 18 children complete work in 2 days. Therefore, (3 x 2) women + (18 x 2) children complete work in 1 days i.e, 6 women + 36 children complete work in 1 day.
Work of 36 children for 1 day = 1 - (1/3) = 2/3
[? work of 6 women for 1 day = 1/3]
? 36 children do 2/3 part of the work in 1 day.
36 children can do the work in 3/2 days.
9 children can do the the work in (3/2) x 4 = 6 days
Correct Answer: 3
Explanation:
Let extra hours a day are N.
According to the formula,
(M1D1T1) / W1 = (M2D2T2) / W2
? [1 x 1 x (6 + 4)] / 1 = [1 x 1 x (6 + 6 + N)] / 11/2
? (3/2) x 10 = 12 + N
? 15 = 12 + N
? N = 15 - 12 = 3
Extra hours of works everyday are 3.
Correct Answer: 2
Explanation:
Here, a1 = 14, b1 = 12, p = 4, a2 = 8, b2 = 16 and q = 5
One days work of 1 man/One days of 1 boy
= (qb2 - pb1) / ( pa1 - qa2)
= [5 x 16 - 4 x 12] / [ 4 x 14 - 5 x 8]
= (80 - 48) / (56 - 40)
= 32/16
= 2
Correct Answer: 9 days
Explanation:
Let the work lasted for N days,
Then, Rashmi's 4 day's work + Ravina (N - 3) day's + Gitika's N day's work = 1
? (4/16) + (N - 3) / (124/5) + N/32 = 1
? 5(N - 3)/64 + N/32 = 1 - 1/4
? [5(N - 3) + 2N] / 64 = 3/4
? 7N - 15 = 48
? N= (48 + 15)/7 = 63/7 = 9 days
Correct Answer: 20 hr
Explanation:
Part filled A in 1 hr= (1/45)
Part filled B in 1 hr= (1/36)
Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20
So, The tank will be full in 20 hr.
Correct Answer: 1/6
Explanation:
We know that, when a pipe fills a tank in m h, then the part of tank filled in 1 h = 1/m
Here, m = 6
? Required part of the tank to be filled in 1h = 1/6 part
Correct Answer: 40 hrs.
Explanation:
Work done by leak in 1 hour = (1/8 - 1/10) = 1/40
? The leak will empty the cistern in 40 hours.
Correct Answer: None of these
Explanation:
Required answer = (12 x 16) /(12 + 16) = 48 / 7 = 66/7 minutes.
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