pool can be filled in 4 hours and drained 5 hours.
take lcm of two pipes that is 20 units.
takes 20 hours to fill pool if both the pipes opened simultaneously.

filling pipe can fill 5units/hour.

draing pipe take out 4units?hour.
pool was opened at 1 pm.
pool was filled at 11 pm. It takes 10 hours to complete it.

If drain pipe opened at 2 pm. filling pipe worked for 1 hour. so 5units work over.
remaining 15 units take additional 15 hours to fill.
if drain pipe opened at 2.30pm. filling pipe worked for 1 and 1/2 hour 7.5 units work over.
take 12. 5 units , take additional 12.5 hours to fill.
if drain pipe opened at 3 pm, 10 units units, over, 10 hours to fill.
if drain pipe opened at 3.30pm. 12.5 units over, another 7.5 units , hours take to fill.
3.30+7.30= 11pm
so option D is correct

I would rather use here smart numbers....
Pool Capacity = 100 Liters
Filling Rate (F) = \(\frac{100}{4}=25\)
Draining Rate (D) = \(\frac{100}{5}=20\)
Time =10 Hours (Start 1:00 pm End 11:00 pm)

250 Liters were filled in 10 hours --> 10*Rate(F) so we have +150 Liters that must be drained (because the filled pool must have only 100 Liters)
\(Rate (D) * t = 150\) --> \(20*t=150\), \(t=7.5 Hours\)
Answer D (11 pm - 7.5 =3:30)

Hope this approach helps....

The valve was opened from 1:00 pm to 11:00 pm, so for 11 - 1 = 10 hours. If x is the amount of time when only the valve was open, then 10 - x is the amount of time when both the valve and the drain were open.
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Solution

Given:

• The pool can be filled in 4 hours
• The pool can be drained in 5 hours.
• Filling valve was opened at 1:00 pm
• The Pool was filled at 11:00 pm

Working out:

We need to find out the time when the drain valve was opened.

Per our conceptual knowledge, we know that the total volume of the pool can be taken as the LCM of 4 and 5.

Thus, let’s assume that the total volume of the pool = 20 Liters.

Since the pool can be filled in 4 hours, in 1 hour, the amount of water filled in it = 5 litres.
Similarly, the amount of water drained in 1 hour = 4 litres.

Let’s also assume that the time after which the drain valve was opened = x hours.
So, from 1 pm to (1+x) pm, the pool was being filled at the rate of 5 liters per hour.
And from (1+x) pm to 11 pm, the pool was filled at a rate of (5-4) = 1 liter per hour.

Thus,

• 5*x+ 1(10-x) = 20
• Or, 5x + 10 -x = 20
• Or, 4x = 10
• Or, x =2.5 hours.

Thus, the drain valve was opened at 1+ 2:30 hours = 3:30 pm.

Answer: Option D
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Let the capacity be 100 litres

Filling rate-20/hr
draining rate: -25 /hr

Filling pipe worked for 10 hours
Thus, 25*10=250
But, capacity is 100

150 must be drained by draining pipe
Thus, it will take 150/20=7.5 hours to drain

Thus, it has started 2.5 hours after 1 pm

Thus, answer=3:30PM