A set (Set ‘P’) of 4 pipes can fill ______% of a tank in 5 minutes while another of set (Set ‘Q’) of 5 pipes can empty the 60% of completely filled tank in 20 minutes. The time taken to fill ________% of tank when the all the pipes of both sets are opened is 4 minutes.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:

I. 80, 52

II. 64, 38.2

III. 75, 48

Solution

For I: For pipes of Set ‘P’: Amount of tank filled by 4 pipes in 5 minutes = 80% Amount of tank filled by 4 pipes in 1 minute = 80/5 = 16% For pipes of set ‘Q’: Amount of tank emptied by 5 pipes in 20 minutes = 60% Amount of tank emptied by 5 pipes in 1 minute = 60/20 = 3% Therefore, effective amount of tank filled by all the pipes of both sets in each minute = 16 – 3 = 13% Therefore, amount of tank filled in 4 minutes = 4 × 13 = 52% Therefore, I is true. For II: For pipes of Set ‘P’: Amount of tank filled by 4 pipes in 5 minutes = 64% Amount of tank filled by 4 pipes in 1 minute = 64/5 = 12.8% For pipes of set ‘Q’: Amount of tank emptied by 5 pipes in 20 minutes = 60% Amount of tank emptied by 5 pipes in 1 minute = 60/20 = 3% Therefore, effective amount of tank filled by all the pipes of both sets in each minute = 12.8 – 3 = 9.8% Therefore, amount of tank filled in 4 minutes = 4 × 9.8 = 39.2% Therefore, II is false. For III: For pipes of Set ‘P’: Amount of tank filled by 4 pipes in 5 minutes = 75% Amount of tank filled by 4 pipes in 1 minute = 75/5 = 15% For pipes of set ‘Q’: Amount of tank emptied by 5 pipes in 20 minutes = 60% Amount of tank emptied by 5 pipes in 1 minute = 60/20 = 3% Therefore, effective amount of tank filled by all the pipes of both sets in each minute = 15 – 3 = 12% Therefore, amount of tank filled in 4 minutes = 4 × 12 = 48% Therefore, III is true