1.
Ram completes 60% of a task in 15 days and then takes the help of Rahim and Rachel. Rahim is 50% as efficient as Ram is and Rachel is 50% as efficient as Rahim is. In how many more days will they complete the work?
Correct Answer
C. 5.71
Explanation
Ram completes 60% of the task in 15 days, which means he completes 1% of the task in 0.25 days. Rahim is 50% as efficient as Ram, so he completes 0.5% of the task in 0.25 days. Rachel is 50% as efficient as Rahim, so she completes 0.25% of the task in 0.25 days. Together, Ram, Rahim, and Rachel complete 1.75% of the task in 0.25 days. To complete the remaining 40% of the task, they will need (40/1.75) * 0.25 = 5.71 days. Therefore, they will complete the work in 5.71 more days.
2.
A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?
Correct Answer
B. 4
Explanation
If all the pipes are kept open, the tank will empty in 6 hours. Each fill pipe takes 8 hours to fill the tank, while each waste pipe takes 6 hours to empty it. Since the tank empties in 6 hours, the combined effect of the waste pipes must be greater than the combined effect of the fill pipes. Therefore, there must be more waste pipes than fill pipes. Since there are a total of 8 pipes, and the number of fill pipes and waste pipes must add up to 8, there must be 4 fill pipes and 4 waste pipes. Thus, the answer is 4.
3.
Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?
Correct Answer
B. 5 days
Explanation
The given information states that A and B can complete the job in 6 days, B and C can complete it in 10 days, and C and A can complete it in 7.5 days. This implies that A, B, and C have different individual work rates. To find the time it takes for all three to complete the job together, we can use the concept of work rates. Let's assume that A's work rate is x, B's work rate is y, and C's work rate is z. From the given information, we can set up the following equations: 1/x + 1/y = 1/6, 1/y + 1/z = 1/10, and 1/z + 1/x = 1/7.5. Solving these equations simultaneously will give us the values of x, y, and z. Then, we can find the total work rate when A, B, and C work together by adding their individual work rates: x + y + z. Finally, we can determine the time it takes for them to complete the job together by dividing the total work required by the total work rate, which gives us 5 days.
4.
Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if A, alone to complete the job?
Correct Answer
C. 10 days
Explanation
The question provides information about how long it takes for different combinations of workers to complete the job. We can use this information to determine how long it would take for A to complete the job alone. Let's assign variables to represent the time it takes for each worker to complete the job alone. Let's say A takes x days, B takes y days, and C takes z days. From the given information, we can create the following equations:
1/x + 1/y = 1/6 (A and B together take 6 days to complete the job)
1/y + 1/z = 1/10 (B and C together take 10 days to complete the job)
1/x + 1/z = 1/7.5 (A and C together take 7.5 days to complete the job)
Solving these equations, we find that x = 10. Therefore, it would take A 10 days to complete the job alone.
5.
Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?
Correct Answer
C. 54 days
Explanation
When four men and three women work together, they can complete the job in 6 days. This means that the total work done by all seven individuals in one day is equal to one-sixth of the total work.
When five men and six women work together, they complete the job in 4 days. This means that the total work done by all eleven individuals in one day is equal to one-fourth of the total work.
To find out how long a woman will take to do the job alone, we need to determine the proportion of work done by a woman in one day.
Let's assume that a woman completes the job alone in x days.
From the given information, we can set up the following equation:
(4/6) + (3/6) = 1/x
Simplifying the equation, we get:
7/6 = 1/x
Cross-multiplying, we find:
7x = 6
Dividing both sides by 7, we get:
x = 6/7
Therefore, a woman will take approximately 0.857 days to complete the job alone, which is equivalent to 0.857 * 24 = 20.57 hours.
Since the answer options are given in terms of days, the closest option is 54 days.
6.
Shyam can do a job in 20 days, Ram in 30 days and Singhal in 60 days. If Shyam is helped by Ram and Singhal every 3^{rd} day, how long will it take for them to complete the job?
Correct Answer
C. 15 days
Explanation
Shyam can complete 1/20th of the job in a day, Ram can complete 1/30th of the job in a day, and Singhal can complete 1/60th of the job in a day. Every 3rd day, Shyam is helped by Ram and Singhal, so the combined work done on those days is 1/20 + 1/30 + 1/60 = 1/10th of the job. Therefore, in 10 days, they can complete 1/10th of the job. Since they need to complete the entire job, it will take them 10 times longer, which is 10 * 10 = 100 days. However, since they work together every 3rd day, the total number of working days will be less than 100. The closest option is 15 days, which is the correct answer.
7.
Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?
Correct Answer
D. 10 hours
Explanation
When pipe A is functioning normally, it takes 2 hours to fill the tank. However, due to the leak at the bottom of the tank, it takes an additional 30 minutes (or half an hour) to fill the tank. This means that the leak is causing a loss of water that would have been filled in that extra 30 minutes. Therefore, the leak is emptying the tank at the same rate that pipe A fills it, which is 2 hours. So, if pipe A is shut, the leak will take 10 hours to empty the full tank.
8.
A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work (in days).
Correct Answer
D. 4
Explanation
A, B, and C can do a total of 1/5 + 1/10 + 1/15 = 1/3 of the work per day. After 2 days, they have completed 2/3 of the work. Since C is the only one left, he will need to do the remaining 1/3 of the work on his own. Since C can do 1/15 of the work per day, it will take him 1/(1/15) = 15 days to complete the remaining work. Therefore, the correct answer is 4.
9.
X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?
Correct Answer
B. Rs. 120
Explanation
X can do 1/15th of the work in one day and Y can do 1/10th of the work in one day. Together, they can do 1/15 + 1/10 = 1/6th of the work in one day. Since they finished the work in 5 days, the total work is 5 * 1/6 = 5/6. The remaining 1/6th of the work was done by Z. Since they were paid Rs. 720 for the entire work, Z was paid 1/6 * Rs. 720 = Rs. 120. Therefore, Z was paid Rs. 120.
10.
A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?
Correct Answer
B. 7
Explanation
A and B can do the work in 1/21 and 1/24 of the work per day respectively. If they work together for x days, they would have completed x/21 + x/24 of the work. After A leaves, B completes the remaining work in 9 days, so B can complete 1/24 of the work per day. Therefore, the remaining work is (1 - x/21 - x/24) and it takes B 9 days to complete this remaining work. Solving this equation, we find that x = 7, which means A leaves after 7 days.
11.
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
Correct Answer
A. 18 days
Explanation
A can complete 1/20th of the project in a day, while B can complete 1/30th of the project in a day. When they work together, they can complete (1/20 + 1/30) = 1/12th of the project in a day.
Let the total number of days taken to complete the project be x. Since A quits 10 days before the project is completed, B works alone for the remaining x-10 days.
So, (x-10)/30 = 1/12. Solving this equation, we get x = 18.
Therefore, the project will be completed in 18 days.