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- Question
A mother can do a certain job in x hours. Her daughter takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the mother take to do the job ?
Options- A. 3
- B. 6
- C. 9
- D. 12
- Correct Answer
- 9
ExplanationThe mother completes the job in x hours.
So, the daughter will take 2x hours to complete the same job.In an hour, the mother will complete 1/x of the total job.
In an hour, the daughter will complete 1/2x of the total job.So, if the mother and daughter work together, in an hour they will complete 1/x + 1/2x of the job.
i.e., in an hour they will complete 3/2x of the job.The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6 th of the task in an hour.Equating the two information, we get 3/2x = 1/6
By solving for x, we get 2x = 18 or x = 9.The mother takes 9 hours to complete the job.
- 1. A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement ?
Options- A. 1900
- B. 2100
- C. 1700
- D. 2000 Discuss
- 2. A contractor undertook to complete a piece of work in 120 Days and employed 140 men upon it. At the end of 66 days only half of the work was done,so he put on 25 extra men. By how much time did he exceed the specific time ?
Options- A. 2 days
- B. 3 days
- C. 4 days
- D. 5 days Discuss
- 3. Twelve children take sixteen days to complete a work which can be completed by 8 adults in 12 days. After working for 3 days, sixteen adults left and six adults and four children joined them. How many days will they take to complete the remaining work ?
Options- A. 3 days
- B. 2 days
- C. 6 days
- D. 12 days Discuss
- 4. A woman fills a bucket in 6 minutes. 1845 buckets have to be filled from 8 am. to 9:30 am. How many woman employees should be employed for this task?
Options- A. 111
- B. 117
- C. 123
- D. 139 Discuss
- 5. 9 girls working 7 hours a day can complete a piece of work in 15 day. In how many days can 6 girls working for 9 hours a day, complete the same piece of work?
Options- A. 35/4 days
- B. 17.5 days
- C. 19 3/4 days
- D. 37/3 days Discuss
- 6. Raghu can do a job in 12 days alone and Sam can do the same job in 15 days alone. A third person Aru whose efficiency is two-third of efficiency of both Ram and Shyam together, can do the same job in how many days alone?
Options- A. 10
- B. 12
- C. 13
- D. 15 Discuss
- 7. A can finish a work in 15 days and B can do the same work in 12 days . B worked for 8 days and left the job .In how many days, A alone can finish the remaining work?
Options- A. 6 days
- B. 5 days
- C. 4 days
- D. 3 days Discuss
- 8. In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap. If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of efficiency of 8th tap and 12th tap, respectively?
Options- A. 4:1
- B. 5:3
- C. 16:1
- D. 1:16 Discuss
- 9. Two persons Shyam and Rahim can do a job in 32 days together. Rahim can do the same job in 48 days alone. They started working together and after working 8 days Rahim is replaced by a third person Ram whose efficiency is half that of Rahim. Find in how many days the remaining work will be completed by both Shyam and Ram together?
Options- A. 16 days
- B. 72/5 days
- C. 15 days
- D. 96/5 days Discuss
- 10. If a soldier fires 7 shots from a gun in 12 minutes then find the total number of shots fired by the man in 3/2 hrs.
Options- A. 45
- B. 44
- C. 46
- D. 47 Discuss
Time and Work problems
Search Results
Correct Answer: 1900
Explanation:
Given 2000 ---- 54 days
The provisions for 2000 men for 39 days can be completed by 'm' men for only 20 days.
i.e, 2000 ----- 39 days == m ---- 20 days
=> m x 20 = 2000 x 39
m = 3900
So total men for 20 days is 3900
=> 2000 old and 1900 new reinforcement.
Hence, reinforcement = 1900.
Correct Answer: 2 days
Explanation:
work done=total number of person x number of days;
half of work done = 140 x 66;
For half of remaining work 25 extra men are added.
Therefore, total men for half work remaining = 140 + 25 = 165;
Let 2nd half work will be completed in K days;
140 x 66 = 165 x K
K = 122;
Hence, extra days => 122-120 = 2days.
Correct Answer: 6 days
Explanation:
From the given data,
12 children 16 days work,
One child?s one day work = 1/192.
8 adults 12 days work,
One adult?s one day?s work = 1/96.
Work done in 3 days = ((1/96) x 16 x 3) = 1/2
Remaining work = 1 ? 1/2 = 1/2
(6 adults+ 4 children)?s 1 day?s work = 6/96 + 4/192 = 1/12
1/12 work is done by them in 1 day.
1/2 work is done by them in 12 x (1/2) = 6 days.
Correct Answer: 123
Explanation:
We know that,
Here M1 = 1, D1 = 6 min, W1 = 1 and M2 = M, D2 = 90 min, W2 = 1845
=> M = 123
Correct Answer: 17.5 days
Explanation:
Let the number of days be 'p'
As the work is same, we know that
Where M = Men, D = Days, H = Hours per day
Here M1 = 9, D1 = 15, H1 = 7
M2 = 6, D2 = p, H2 = 9
=> 9 x 15 x 7 = 6 x p x 9
=> p = 35/2 = 17.5 days.
Correct Answer: 10
Explanation:
One day work of Raghu and Sam together = 1/12 + 1/15 = 9/60 = 3/20
Aru efficiency = 2/3 of (Raghu + Sam)
Number of days required for Aru to do thw work alone = 3/2 x 20/3 = 10 days.
Correct Answer: 5 days
Explanation:
B's 8 days work=(1/12) x 8 = 2/3
Reaining work= 1/3
Now, 1/15 work is done by A in 1 day
Therefore, 1/3 work is done by A in 15 x (1/3) = 5 days
Correct Answer: 1:16
Explanation:
Time taken by 8th tap = 2 x 2 x 2= 8 hours
Time taken by 12th tap = 2x (1/2) x (1/2) = 1/2 hour
Ratio of time taken by 8th tap and 12th tap = 8 : 1/2 =16:1
Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16
Correct Answer: 72/5 days
Explanation:
Work done by Shyam and Rahim in 8 days = 8/32 = 1/4
Remaining work to be done by Shyam and Ram = 1 - 1/4 = 3/4
Given efficieny of Ram is half of Rahim i.e, as Rahim can do the work in 48 days, Ram can do the work in 24 days.
One day work of Ram and Shyam = (1/32 - 1/48) + 1/24 = 5/96
Hence, the total work can be done by Shyam and Ram together in 96/5 days.
Therefore, remaining work 3/4 can be done by them in 3/4 x 96/5 = 72/5 = 14.4 days.
Correct Answer: 46
Explanation:
Here given soldier shots 7 shots in 12 min
=> 1 shot doen't take any time in 12 min
=> Only 6 shots take 12 min
12 min ------ 6 shots
90 min ------ ? shots
=> 90 x (6/12) = 45
Therefore, total shots fired in 90 minutes = 45 + 1 = 46 shots.
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