# 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 =$\frac{1}{n}$

**2. **If A’s 1 day's work =$\frac{1}{n}$, 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 :

$Efficiency\propto \frac{1}{Nooftimeunits}$

$\therefore Efficiency\times Time=Cons\mathrm{tan}tWork$

Hence, $Requiredtime=\frac{Work}{Efficiency}$

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 = $\frac{100}{Efficiency}$

A) 4 days | B) 5 days |

C) 6 days | D) 7 days |

Explanation:

Work donee by A and B in the first two hours, working alternatively = First hour A + Second hour B = (1/4) + (1/12) = 1/3.

Thus, the total time required to complete the work = 2 (3) = 6 days

A) Total work | B) One-fourth work |

C) Half work | D) Two-third work |

Explanation:

A can do the work = 18 days

B can do the work = 18/2 = 9 days

(A + B)'s 1 day work = 1/18 + 1/9 = 1/6

=> In 3 days = 3x1/6 = 1/2 work is completed.

A) 15 days | B) 11 days |

C) 14 days | D) 12 days |

Explanation:

9M + 12B ----- 12 days ...........(1)

12M + 12B ------- 10 days........(2)

10M + 10B -------?

108M + 144B = 120M +120B

24B = 12M => 1M = 2B............(3)

From (1) & (3)

18B + 12B = 30B ---- 12 days

20B + 10B = 30B -----? => 12 days.

A) A | B) B |

C) C | D) can't be determined |

Explanation:

A + B= 70%

B + C =50%

$\left[\because (A+B)+(B+C)-(A+B+C)=B\right]$

=> B= 20% A= 50% and C=30%

Hence A is most efficient

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

150 men in 25 days do = $\frac{1}{4}$ work

Let 1 man in 1 day does =** x** work

Total work done by 150 men in 25 days = 150x * 25 = $\frac{1}{4}$ work => x = $\frac{1}{15000}$

Therefore, 100 men in 60 days do = 100 * 60x = **6000x** work = 6/15 = 2/5

Total work done =$\frac{1}{4}+\frac{2}{5}=\frac{13}{20}$

Therefore, Remaining work = 1 - $\frac{13}{20}$ = $\frac{7}{20}$

Remaining time = 130 - (25+60+10) = 35 days

Therefore, work is done in 25 days by 150 men.

Therefore, Work is done in 35 days by 150 men.

Hence, he should employ 50 more men.

A) 4 days | B) 8 days |

C) 3 days | D) 6 days |

Explanation:

4/10 + 9/x = 1 => x = 15

Then both can do in

1/10 + 1/15 = 1/6 => 6 days

A) 1/24 days | B) 7/24 days |

C) 24/7 days | D) 4 days |

Explanation:

(A+B+C)'s 1 day's work = (1/24 + 1/6 + 1/12) = 7/24

so, A,B and C together will complete the work in 24/7 days.