Multiple choice

Pipe A and B fill a tank in 90 hours and 60 hours respectively.If the capacity of the tank is increased by 40% and both pipes start working at 80% of their efficiency, now in what time tank will be completely filled ?

  1. 63 hours

  2. 52 hours

  3. 65 hours

  4. 48 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original: A fills in 90 hrs (rate = 1/90), B fills in 60 hrs (rate = 1/60). Combined rate = 1/90 + 1/60 = 5/180 = 1/36. Time for original tank = 36 hrs. New capacity = 1.4× original. New rates (80% efficiency): A = 0.8/90 = 1/112.5, B = 0.8/60 = 1/75. Combined new rate = 1/112.5 + 1/75 = 5/450 + 6/450 = 11/450. New time = 1.4 / (11/450) = 1.4 × 450/11 = 630/11 = 57.27... Hmm, not 63. Let me recalculate: Original combined time = 1/(1/90 + 1/60) = 1/(5/180) = 36 hrs. With 80% efficiency, new rates are 0.8× original. New combined rate = 0.8 × (1/90 + 1/60) = 0.8/36 = 1/45. For 1.4× capacity, time = 1.4 × 45 = 63 hrs. Yes! Matches option A exactly.

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