CAT 2018Slot 2QAQuestion & Solution
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 filling 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 filled on Thursday if both pumps were used simultaneously all along?
Options
4:48 pm
4:12 pm
4:24 pm
4:36 pm
Solution
Let 't' pm be the time when the tank is emptied everyday. Let 'a' and 'b' be the liters/hr filled by pump A and pump B respectively.
On Monday, A alone completed filling the tank at 8 pm. Therefore, we can say that pump A worked for (8 - t) hours. Hence, the volume of the tank = a(8 - t) liters.
Similarly, on Tuesday, B alone completed filling the tank at 6 pm. Therefore, we can say that pump B worked for (6 - t) hours. Hence, the volume of the tank = b(6 - t) liters.
On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. Therefore, we can say that pump A worked for (5 - t) hours and pump B worked for 2 hours. Hence, the volume of the tank = a(5 - t)+2b liters.
We can say that a(8 - t) = b(6 - t) = a(5 - t) + 2b
a(8 - t) = a(5 - t) + 2b
$\Rightarrow 3a = 2b$ ... (1)
a(8 - t) = b(6 - t)
Using equation (1), we can say that
$a(8-t) = \dfrac{3a}{2} \times (6-t)$
$t = 2$
Therefore, we can say that the tank gets emptied at 2 pm daily. We can see that A takes 6 hours and pump B takes 4 hours alone.
Hence, working together both can fill the tank in = $\dfrac{6 \times 4}{6+4} = 2.4$ hours or 2 hours and 24 minutes.
The pumps started filling the tank at 2:00 pm. Hence, the tank will be filled by 4:24 pm.