Question:
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed ?lling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank ?lled on Thursday if both pumps were used simultaneously all along?
A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed ?lling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank ?lled on Thursday if both pumps were used simultaneously all along?
Updated On: Sep 30, 2024
- 4:36 pm
- 4:12 pm
- 4:24 pm
- 4:48 pm
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The Correct Option is C
Solution and Explanation
The correct answer is (C):
Let x be the time, on a 24 hours clock, at which the tank is empty.
Time taken by pipe A alone to fill the tank is (20 – x) hrs.
Time taken by pipe B alone to fill the tank is (18 – x) hrs.
On the other day, A fill the tank for (15 – x) hrs and B for 2 hrs.
Let A and B be the rate of works of pipe A and B respectively.
⇒ (20-x)A = (18-x)B = (17-x)A+2B
⇒ A/B = 2/3
⇒ (20-x)2 = (18-x)3
⇒ (20-x)A = 1
Let (20-x)A = 1
A = 1/6
B = 1/4
When both work simultaneously, time taken
= 1/1/6+1/4 = 2.4hrs = 2hrs24min
The tank will be filled by 16: 24i.e..4: 24pm
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