# Time and Work Questions

**FACTS AND FORMULAE FOR TIME AND WORK QUESTIONS**

**1. **If A can do a piece of work in n days, then A's 1 day's work =

**2. **If A’s 1 day's work =, then A can finish the work in n days.

**3. **A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

NOTE :

Hence,

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours =

A) 3 hrs | B) 6 hrs |

C) 7 hrs | D) 5 hrs |

Explanation:

Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.

Then, (1/x + 2/x + 3/x) = 1/2

6/x = 1/2 => x = 12

So, B takes 6 hours to finish the work.

A) 45 metric tonnes | B) 47 metric tonnes |

C) 55 metric tonnes | D) 34 metric tonnes |

Explanation:

2 engines of former type for one hour consumes 2x24/(6x8) = 1 metric ton

i.e. 3 engines of latter type consumes 1 ton for one hour

hence 9 engines consumes 3 tons for one hour

for 15 hours it is 15 x 3 = 45 metric tonnes.

A) 120 days | B) 119 days |

C) 118 days | D) 117 days |

Explanation:

K's work in a day(1st day) = 1/30

L's work in a day(2nd day)= -1/60(demolishing)

hence in 2 days, combined work= 1/30 - 1/60

=1/60

since both works alternatively, K will work in odd days and L will work in even days.

1/60 unit work is done in 2 days

58/60 unit work will be done in 2 x 58 days = 116 days

Remaining work = 1-58/60

= 2/60

= 1/30

Next day, it will be K's turn and K will finish the remaining 1/30 work.

hence total days = 116 + 1 = 117.

A) 6 | B) 9 |

C) 5 | D) 7 |

Explanation:

Let 1 woman's 1 day work = x.

Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4.

So, (3x/2 + 4x + + 6x/4) = 1/7

28x/4 = 1/7 => x = 1/49

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = 49/7 = 7.

A) 14 1/2 days | B) 11 days |

C) 13 1/4 days | D) 12 6/7 days |

Explanation:

Let 'B' alone can do the work in 'x' days

6/30 + 18/x = 1

x = 22.5

1/30 + 1/22.5 = 7/90

=> 90/7 = 12 6/7 days