kamalakarthi wrote: ↑Tue May 16, 2017 4:33 pm
Hi, In the attached question, I tried to take common value as 24 litres and then I calculated the pipe can drain 6 litres in an hr so when the question says that the tank is emptied in 6 hrs , I calculated the capacity as 36 litres. Is this approach right ? or Is there a better approach to this question. Can you please help.
Solution:
We can let c = the capacity of the pool. We see that the rate of the pipe emptying the pool is c/4 when the pool is full and it’s not raining, and that the rate of the pipe emptying the pool is c/6 when the pool is full and it’s raining. We can create the following equation:
c/4 - 3 = c/6
Multiplying the equation by 12, we have:
3c - 36 = 2c
c = 36
Alternate Solution:
Let r be the number of hours it would take the rain to fill the empty pool. Then, in one hour, the rain fills 1/r of the pool and the pipe empties 1/4 of the pool. Working together, the pool is emptied in 6 hours or, equivalently, 1/6 of the pool is emptied in one hour. Thus, we can create the following equation:
1/4 - 1/r = 1/6
Let’s multiply each side by 12r:
3r - 12 = 2r
r = 12
Thus, it would take the rain 12 hours to fill the empty pool. Then, since rain adds 3 liters of water to the pool each hour, the capacity of the pool is 12 x 3 = 36 liters.
Answer: D
