a. 1.25 pm

b. 12 pm

c. 12.12 pm

d. 12.28 pm

**Answer:** c. 12.12 pm

**Explanation:**

Let the tank get empty in T hours counting from 8 am.

A is on for T hours and work done by A = Work in 1 hour x T hours = | T | = | 2T |

1.5 | 3 |

Similarly, B starts at 9 am i.e. it's on for (T-1) hours & work done is = | T-1 |

2 |

Similarly, C starts at 10 am i.e. for (T-2) hours & work done is = | T-2 | = | 2(T-2) |

1/2 |

∴ | 2T | + | T-1 | - 2(T - 2) = 0 |

3 | 2 |

∴ T = | 21 | hours = 4.2 hours = 4 hours 12 minutes |

5 |

a. 9.75 hours

b. 10. 90 hours

c. 11.25 hours

d. 12.90 hours

**Answer:** c. 11.25 hours

**Explanation:**

Let Pipe A, B and C fill the tank individually in A, B and C hours respectively.

Tank filled by Pipe A, B and C together in 1 hour = | 1 | = | 1 | + | 1 | + | 1 |

5 | A | B | C |

Tank filled by Pipe A and B together in 1 hour = | 1 | = | 1 | + | 1 |

6 | A | B |

Tank filled by C in 1 hour = | 1 | - ( | 1 | + | 1 | ) = | 1 | - | 1 | = | 1 |

6 | A | B | 6 | 5 | 30 |

∴ A = ½B

∴ | 1 | + | 1 | = | 1 |

½B | B | 6 |

∴ | 1 | = | 1 | hours |

B | 18 |

Tank filled by B and C in one hour = | 1 | + | 1 | = | 1 | + | 1 | = | 8 |

B | C | 18 | 30 | 90 |

∴ Tank can be filled in | 90 | = 11.25 hours |

8 |

a. 500 litres

b. 600 litres

c. 1000 litres

d. 1200 litres

**Answer:** b. 600 litres

**Explanation:**

Let Tap A fill the cistern completely in A hours.

So in 1 hour it fills | 1 | amount of the cistern |

A |

Also in 1 hour Tap B fills | 1 | amount of the cistern |

4 |

So, in 1 hour together they'll fill | 1 | amount of the cistern |

2.4 |

Also in 1 hour cistern filled by both is given by | 1 | + | 1 | = | 1 |

A | 4 | 2.4 |

∴ | 1 | = | 1 | - | 1 | = | 1 |

A | 2.4 | 4 | 6 |

∴ Pipe a fills the tank completely in 6 hours.

It has a rate of 100 litre water per hour,

So, in 6 hours it gives out 6 x 100

a. 18 minutes

b. 24 minutes

c. 1 hour 20 minutes

d. 2 hours 15 minutes

**Answer:** b. 24 minutes

**Explanation:**

In 1 hour, tank filled by Pipe P = | 1 |

15 |

In 1 hour, tank filled by Pipe Q = | 1 |

10 |

In 1 hour, tank emptied by Pipe R = | 1 |

30 |

In one hour tank filled = | 1 | + | 1 | = | 5 |

15 | 10 | 30 |

So entire tank gets filled in | 30 | = 6 hours |

5 |

When Pipe P, Q & R is open, in 1 hour tank filled = | 1 | + | 1 | - | 1 | = | 4 |

15 | 10 | 30 | 30 |

In 2 hours, 2 x | 4 | = | 8 | amount of tank is filled |

30 | 30 |

Remaining tank = 1 - | 8 | = | 22 |

30 | 30 |

In 1 hour, | 5 | amount of tank is filled |

30 |

In ? hours, | 22 | amount of tank is filled |

30 |

∴ ? hours = | 22/30 | = | 22 | = 4.4 hours |

5/30 | 5 |

a. 10 hours

b. 12 hours

c. 13 hours

d. 14 hours

**Answer:** d. 14