# 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) 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) 6 | B) 8 |

C) 9 | D) 12 |

Explanation:

$\begin{array}{ccccc}& & Amit& & Bharat\\ No.ofDays& & 45& & 40\\ Efficiency& & 2.22Percent(=\frac{1}{45})& & 2.5Percent(=\frac{1}{40})\end{array}$

Amit did the work in 56 days = $56\times \frac{1}{45\times 2}=\frac{28}{45}$

Therefore, Rest work 17/45 was done by Amit and Bharath = $\frac{{\displaystyle \raisebox{1ex}{$17$}\!\left/ \!\raisebox{-1ex}{$45$}\right.}}{{\displaystyle \raisebox{1ex}{$17$}\!\left/ \!\raisebox{-1ex}{$360$}\right.}}$ = 8 days

( since Amit and Bharath do the work in one day = $\frac{1}{45}+\frac{1}{40}=\frac{17}{360}$)

A) 3 hours | B) 4 hours |

C) 5 hours | D) None of these |

Explanation:

Rate of leakage = 8.33% per hour

Net efficiency = 50 - (16.66 + 8.33)= 25%

Time required = 100/25 = 4 hours

A) 60 | B) 70 |

C) 80 | D) 90 |

Explanation:

Let A's 1 day's work=x and B's 1 day's work=y

Then x+y = 1/40 and 20x+60y=1

Solving these two equations , we get : x= 1/80 and y= 1/80

Therefore B's 1 day work = 1/80

Hence,B alone shall finish the whole work in 80 days

A) 1 day | B) 2 days |

C) 5 days | D) None of these |

Explanation:

Total work = 100+50 = 150man-days

In 8 days 100 man-days work has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man- days work. Thus the work requires 2 more days.

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) 40 days | B) 36 days |

C) 32 days | D) 34 days |

Explanation:

Let 1 man's 1 day work = x and 1 woman's 1 day work = y.

Then, 4x + 6y = 1/8 and 3x + 7y = 1/10

Solving these two equations, we get:

x = 11/400 and y = 1/400

10 woman's 1 day work = (1/400 x 10) = 1/40.

Hence, 10 women will complete the work in 40 days.

A) 15 | B) 30 |

C) 25 | D) 10 |

Explanation:

Combined efficiency of all the three boats = 60 passenger/trip

Now, consider option(a)

15 trips and 150 passengers means efficiency of B1 = 10 passenger/trip

which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (10-5 = 5) in which B2 and B3 together carried remaining 250 (300 - 50 = 250) Passengers.

Therefore the efficiency of B2 and B3 = 250/5 = 50 passenger/trip

Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct.