Time and Work Question 6 - CAT 2021
Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is:
Step-by-Step Explanation
Let Pipe A's filling rate be a units/hour and Pipe B's draining rate be b units/hour.
- Case 1:
Pipe A opens at 2 PM and runs until 10 PM (8 hours).
Pipe B opens at 3 PM and runs until 10 PM (7 hours).
Tank Capacity = 8a − 7b --- (Equation 1)
- Case 2:
Pipe A opens at 2 PM and runs until 6 PM (4 hours).
Pipe B opens at 4 PM and runs until 6 PM (2 hours).
Tank Capacity = 4a − 2b --- (Equation 2)
- Equate the two capacity expressions to find the relationship between a and b:
8a − 7b = 4a − 2b
⟹ 4a = 5b
⟹ b = 0.8a
- Substitute b = 0.8a back into Equation 2 to find the total capacity in terms of a:
Tank Capacity = 4a − 2(0.8a)
= 4a − 1.6a
= 2.4a
If Pipe B is kept closed, only Pipe A operates to fill the tank:
Time required = Tank Capacity/a
= 2.4a/a
= 2.4 hours
Time in minutes = 2.4 × 60
= 144 minutes
Correct Option: A