Pipes And Cisterns Aptitude Quiz

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.