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- Question
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
- Correct Answer
- 72/5 days
ExplanationWork 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.
- 1. 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
- 2. 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
- 3. 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
- 4. 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 Discuss
- 5. 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
- 6. 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
- 7. A certain job was assigned to a group of women to do it in 20 days. But 12 women did not turn up for the job and the remaining did the job in 32 days. The original number of women in the group was?
Options- A. 36
- B. 32
- C. 22
- D. 28 Discuss
- 8. One girl can eat 112 chocolates in half a minute, and her boy friend can eat half as many in twice the length of time. How many chocolates can both boy and girl eat in 12 seconds ?
Options- A. 44
- B. 32
- C. 56
- D. 49 Discuss
- 9. K can build a wall in 30 days. L can demolish that wall in 60 days. If K and L work on alternate days, when will the wall be completed ?
Options- A. 120 days
- B. 119 days
- C. 118 days
- D. 117 days Discuss
- 10. Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work ?
Options- A. 18 days
- B. 20 days
- C. 16 days
- D. 14 days Discuss
Time and Work problems
Search Results
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: 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: 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: 9
Explanation:
The 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.
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: 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.
Correct Answer: 32
Explanation:
Let the total women in the group be 'W'
Then according to the given data,
W x 20 = (W-12) x 32
=> W = 32
Therefore, the total number of women in the group = 32
Correct Answer: 56
Explanation:
Girl eats 112 chocolates in 30 sec
so she can eat in 12 sec is 12 x 112/30 = 44.8 chocolates.
Her boy friend can eat one-half of 112 in twice of 30 sec
so he can eat 56 in 60 sec
Then he can eat in 12 sec is 56 x 12/60 = 11.2 chocolates.
Hence, together they can eat = 44.8 + 11.2 =56 chocolates in 12 seconds.
Correct Answer: 117 days
Explanation:
K's work in a day(1st day) = 1/30
L's work in a day(2nd day)= -1/60(demolishing)
hence in 2 days, combined work= 1/30 - 1/60 =1/60
since both works alternatively, K will work in odd days and L will work in even days.
1/60 unit work is done in 2 days
58/60 unit work will be done in 2 x 58 days = 116 days
Remaining work = 1-58/60 = 1/30
Next day, it will be K's turn and K will finish the remaining 1/30 work.
hence total days = 116 + 1 = 117.
Correct Answer: 20 days
Explanation:
(5m + 9w)10 = (6m + 12w)8
=> 50m + 90w = 48w + 96 w => 1m = 3w
5m + 9w = 5m + 3m = 8m
8 men can do the work in 10 days.
3m +3w = 3m + 1w = 4m
So, 4 men can do the work in (10 x 8)/4 = 20 days.
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