In the kitchen there are two pipes A and B. Pipe B take 5 more minutes than Pipe A to fill a vessel. While the two Pipes A and B when opened together can fill the vessel in 6 minutes, then find time in which A and B can fill the tank separately will be respectively?
Options
15 minutes, 10 Minutes.
15 minutes, 20 Minutes.
10 minutes, 15 minutes.
20 minutes, 15 Minutes.
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A and B can fill the tank separately in 10 & 15 mins respectively
Step-by-step explanation:
Pipe A can fill a vessel in A mins
then pipe can fill in 1 min = 1/A
Pipe B take 5 more minutes than Pipe A to fill a vessel
Pipe B can fill in A + 5 Mins
Pipe A & B can fill vessel together in 6 Mins
Pipe A & B can fill vessel in 1 min = 1/6
=> 1/A + 1/(A + 5) = 1/6
=> 6(A + 5) + 6A = A(A + 5)
=> 6A + 30 + 6A = A² + 5A
=> A² - 7A - 30 = 0
=>A² - 10A + 3A - 30 = 0
=> A(A - 10) + 3(A - 10) = 0
=> (A + 3)(A - 10) =0
=> A = 10
Pipe A can fill in 10 mins
Pipe B can fill in 10 + 5 = 15 mins
A and B can fill the tank separately in 10 & 15 mins respectively
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