Question : Two taps A and B can fill a tank in 10 hours and 12 hours respectively. If the two taps are opened at 10 AM, at what time (in PM) should tap A be closed to fill the tank at exactly 4 PM?
Option 1: 2:00
Option 2: 3:00
Option 3: 1:00
Option 4: 1:30
Correct Answer: 3:00
Solution : Tap A's hourly work = $\frac{1}{10}$ Tap B's hourly work = $\frac{1}{12}$ (Tap A + Tap B)'s hourly work $=\frac{1}{10}+\frac{1}{12}=\frac{11}{60}$ Let tap A be closed after $x$ hours. Then, part filled by (A + B) in $x$ hours + part filled by B in $(6 -x)$ hours $= 1$ ⇒ $\frac{11x}{60}+\frac{(6–x)}{12}=1$ ⇒ $\frac{11x+30–5x}{60}=1$ ⇒ $6x+30=60$ ⇒ $6x=30$ $\therefore x=5$ After 5 hours, Tap A should be closed i.e, 10:00 AM + 5 hours = 3:00 PM Hence, the correct answer is 3:00.
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Question : There are 3 taps, A, B, and C, in a tank. These can fill the tank in 10 h, 20 h, and 25 h, respectively. At first, all three taps are opened simultaneously. After 2 h, tap C is closed, and taps A and B keep running. After 4 h, tap B is also closed. The remaining tank is filled by tap A alone. Find the percentage of work done by tap A itself.
Option 1: 75%
Option 2: 52%
Option 3: 72%
Option 4: 32%
Question : Directions: A tap can fill up a tank of 1250 litres in 4 hours, whereas another tap can fill the same tank in 8 hours. An outlet tap can empty that tank in 6 hours. If all three taps are opened simultaneously, then how much time will it take to fill the tank?
Option 1: 4.2 Hours
Option 2: 5 Hours
Option 3: 4.5 Hours
Option 4: 4.8 Hours
Question : Taps A and B can fill a tank in 15 minutes and 10 minutes, respectively while tap C can empty the full tank in x minutes. If all three taps are opened together, the tank is filled completely in 8 minutes. Tap C alone will empty $\frac{3}{8}$ th part of the tank in:
Option 1: 10 minutes
Option 2: $10 \frac{1}{2}$ minutes
Option 3: 9 minutes
Option 4: $8 \frac{1}{2}$ minutes
Question : Pipes A, B and C can fill a tank in 10, 15 and 30 hours, respectively. D is an emptying pipe which alone can empty the full tank in $x$ hours. A, B and C are opened together for 3 hours and then closed. Now D is opened which alone empties the tank in 30 hours. What is the value of $x$?
Option 1: 50
Option 2: 40
Option 3: 60
Option 4: 45
Question : Pipes P and Q can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all three are opened at 7 AM at what time will one-fourth of the tank be filled?
Option 1: 10 AM
Option 2: 10 PM
Option 3: 11 PM
Option 4: 11 AM
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