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A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes, respectively. How many minutes will it take to fill the tanker from empty state, if B is used for half the time and A and B fill it together for the other half?
27.5 min
30 min
15 min
20 min
30 min
Use LCM of 60 and 40 (120 units) to find rates. Efficiency of A = 2, B = 3. Set up the equation (B's rate) * (t/2) + (A+B's rate) * (t/2) = 120.
Pipe A fills in 60 min, Pipe B in 40 min. B runs for half the total time (t/2), and A+B run for the other half (t/2).
W=R├Чt
Use LCM of 60 and 40 (120 units) to find rates. Efficiency of A = 2, B = 3. Set up the equation (B's rate) * (t/2) + (A+B's rate) * (t/2) = 120.
Students often assume A runs for half the time and B runs for the full time, but the question states B runs for half and (A+B) run for half.
Calculate Rates
Assuming total capacity is the LCM of 60 and 40, which is 120 units. Rate of Pipe A = 120/60=2 units/min. Rate of Pipe B = 120/40=3 units/min.
RAтАЛ=2,RBтАЛ=3
Set up equation for Total Work
Let the total time be t. Pipe B runs for t/2 and (Pipe A + Pipe B) run for the remaining t/2.
3├Ч2tтАЛ+(2+3)├Ч2tтАЛ=120
Solve for t
Simplify the equation: 1.5t+2.5t=120тЗТ4t=120.
t=4120тАЛ=30
B is correct because the total time required is 30 minutes.
This is equivalent to the 'Time and Work' topic where efficiency is additive; always calculate efficiency first when dealing with multiple workers or pipes.
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