Question
Pipe A can fill a tank in 45 minutes while pipe B can
fill it in ____ minutes. There’s a leak in the tank which can empty it in _____minutes. When both the pipes are open, due to the effect of the leak, the tank gets filled in 30 minutes. Which of the following values can fill the blanks in the same order? I. 60, 80 II. 70, 50 III. 45, 90 IV. 36, 60Solution
From I: Portion of tank filled in a minute = 1/45 + 1/60 - 1/80 = (16 + 12 – 9)/720 = 19/720 Hence, I does not follow From II: Portion of the tank filled in a minute 1/45 + 1/70 – 1/50 = (70+45-63)/3150 = 52/3150 Hence II also does not follow. From III: Portion of the tank filled in a minute. = 1/45 + 1/45 – 1/90 = (2 + 2 – 1)/90 = 3/90 = 1/30 From IV: Portion of the tank filled in a minute = 1/45 + 1/36 – 1/60 = (4 + 5 – 3)/180 = 6/180 = 1/30 Hence only III and IV satisfy the given blanks.
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