A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?
- A8 minutes
- B10 minutes
- C12 minutes
- D16 minutesCorrect
Explanation
To find the time taken to fill 50 percent of the tank, we first calculate the efficiency of each set of pipes.
Set X: 20 pipes fill 70 percent in 14 minutes. This means 20 pipes fill 5 percent per minute. If only half the pipes (10 pipes) are open, they will fill 2.5 percent per minute.
Set Y: 10 pipes fill 3/8th (37.5 percent) in 6 minutes. This means 10 pipes fill 6.25 percent per minute. If only half the pipes (5 pipes) are open, they will fill 3.125 percent per minute.
Set Z: 16 pipes empty 50 percent in 20 minutes. This means 16 pipes empty 2.5 percent per minute.
Now, we combine the rates of the active pipes: Net Rate = (Rate of 10 pipes from X) + (Rate of 5 pipes from Y) - (Rate of 16 pipes from Z) Net Rate = 2.5 + 3.125 - 2.5 = 3.125 percent per minute.
To fill 50 percent of the tank at a rate of 3.125 percent per minute: Time = 50 divided by 3.125 = 16 minutes.
Therefore, it will take 16 minutes to fill 50 percent of the tank. The correct option is D.
Related questions
More UPSC Prelims practice from the same subject and topic.
- Prelims 2025CSATQuantitative Aptitude
X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n d…
- Prelims 2025CSATQuantitative Aptitude
A natural number N is such that it can be expressed as N = p + q + r , where p, q and r are distinct factors of N. How many numbers below 50 have this property?
- Prelims 2025CSATQuantitative Aptitude
Three prime numbers p, q and r, each less than 20, are such that p - q = q - r . How many distinct possible values can we get for (p + q + r) ?
- Prelims 2025CSATQuantitative Aptitude
How many possible values of (p + q + r) are there satisfying (1)/(p) + (1)/(q) + (1)/(r) = 1 , where p, q and r are natural numbers (not necessarily distinct)?
- Prelims 2025CSATQuantitative Aptitude
Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had team Y's average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How ma…
- Prelims 2025CSATQuantitative Aptitude
The price (p) of a commodity is first increased by k% ; then decreased by k% ; again increased by k% ; and again decreased by k% . If the new price is q , then what is the relation between p and q ?