Question : Two pipes can fill a tank in 20 minutes and 30 minutes, respectively. When the tank was empty, the two pipes were opened. After some time, the first pipe was stopped, and the tank was filled in 18 minutes. After how much time had passed since the start, was the first pipe stopped?
Option 1: 5 minutes
Option 2: 8 minutes
Option 3: 10 minutes
Option 4: 12 minutes
Correct Answer: 8 minutes
Solution :
Let the total capacity of the tank = LCM of 20 and 30
= 60 units
Efficiency of first pipe = $\frac{60}{20}$ = 3
Efficiency of second pipe = $\frac{60}{30}$ = 2
After $x$ minutes the first pipe was stopped, the first pipe worked for $x$ minutes and the second pipe worked for 18 minutes.
Therefore, 3 × $x$ + 18 × 2 = 60
⇒ 3$x$ = 24
⇒ $x$ = 8 minutes
Hence, the correct answer is 8 minutes.
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