আমাদের স্কুলের চৌবাচ্চায় দুটি নল আছে। নল দুটি দিয়ে চৌবাচ্চাটি 110 মিনিটে পূর্ণ হয়। যদি নলদুটি
আলাদাভাবে খােলা থাকে তবে চৌবাচ্চাটি ভর্তি করতে একটি নল অপর নলটি থেকে 5 মিনিট বেশি।
Answers
Given : Tank is filled by two pipes in 110 minutes
one pipe take 5 minute extra then other if filled separately
To Find : Time taken by each pipe to fill tank separately
Solution:
Pipe A fill in T minutes
Pipe B fill in T + 5 minutes
Pipe A fill in 1 minute = 1/T
Pipe B fill in 1 minute = 1/(T + 5)
Together fill in 1 min = 1/T + 1/(T + 5)
Tank is filled in 110 minutes
=> Filled in 1 minute = 1/110
1/T + 1/(T + 5) = 1/110
=> 110(T + 5) + 110T = T(T + 5)
=> 220T + 550 = T² + 5T
=> T² - 215T - 550 = 0
on solving
T = -2.53 , 217.53
217.53 Minutes
222.53 Minutes
If Question is Tank is filled in 11 1/9 = 100/9 minutes
=> Filled in 1 minute = 9/110
1/T + 1/(T + 5) = 9/100
=> 100(T + 5) + 100T = 9T(T + 5)
=> 200T + 500 = 9T² + 45T
=> 9T² - 155T - 500 = 0
=> 9T² - 180T + 25T - 500 = 0
=> 9T(T - 20) + 25(T - 20) = 0
=> (9T + 25)(T - 20) = 0
=> T = 20 as T can not be negative
20 and 25 minutes will be taken by pipes.
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