# 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) 9 days | B) 11 days |

C) 13 days | D) 15 days |

Explanation:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x => x = ( 23 x 13/10 ) => x = 299 /10.

A's 1 day's work = 1/23 ;

B's 1 day's work = 10/299 .

(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 113 .

Therefore, A and B together can complete the work in 13 days.

(A+B)'s two days work = $\frac{1}{40}+\frac{1}{50}=\frac{9}{200}$

Evidently, the work done by A and B duing 22 pairs of days

i.e in 44 days = $22\times \frac{9}{200}=\frac{198}{200}$

Remaining work = $1-\frac{198}{200}$= 1/100

Now on 45th day A will have the turn to do 1/100 of the work and this work A will do in $40\times \frac{1}{100}=\frac{2}{5}$

Therefore, Total time taken = 44$\frac{2}{5}$daya

A) 4 days | B) 6 days |

C) 7 days | D) 5 days |

Explanation:

Given that

6 men and 8 boys can do a piece of work in 10 days

26 men and 48 boys can do the same in 2 days

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

=> M = 2B

=> B = M/2 ……(1)

Now Put (1) in 15M + 20B

=> 15M + 10M = 25M

Now, 6M + 8B in 10 days

=> (6M + 4M) 10 = 100M

Then D(25M) = 100M

=> D = 4 days.

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) 12 days | B) 18 days |

C) 24 days | D) 30 days |

Explanation:

A + B = C + D

| | | |

Ratio of efficiency 10x + 5x 9x + 6x

|________| |_________|

15x 15x

Therefore , ratio of efficiency of A:C =10:9

Therefore, ratio of days taken by A:C = 9:10

Therefore, number of days taken by A = 18 days

A) 17 + 4/7 days | B) 13 + 1/3 days |

C) 15 + 3/2 days | D) 16 days |

Explanation:

C alone can finish the work in 40 days.

As given C does half as much work as A and B together

=> (A + B) can do it in 20 days

(A + B)s 1 days wok = 1/20.

A's 1 days work : B's 1 days Work = 1/2 : 1 = 1:2(given)

A's 1 day’s work = (1/20) x (1/3) = (1/60) [Divide 1/20 in the raio 1:2]

B's 1 days work = (1/20) x (2/3) = 1/30

(A+B+C)'s 1 day's work = (1/60) + (1/30) + (1/40) = 9/120 = 3/40

All the three together will finish it in 40/3 = 13 and 1/3 days.

A) 50 | B) 40 |

C) 45 | D) 10 |

Explanation:

Let the number of workers be x.

Now, Using work equivalence method,

X + (X-1) + (X-2)+ . . . . + 1 = X *55% of X

=> [X * (X+1)] / 2 = X * (55X/100) [because, Series is in AP. Sum of AP = {No. of terms (first term+ last term)/2} ]

Therefore, X = 10

A) 20days | B) 40 days |

C) 50 days | D) 60 days |

Explanation:

(A+B)'s 1 day's work=1/20

C's 1 day work=1/60

(A+B+C)'s 1 day's work= 1/20 + 1/60 = 1/15

Also A's 1 day's work =(B+C)'s 1 day's work

Therefore, we get: 2 x (A's 1 day 's work)=1/15

=>A's 1 day's work=1/30

Therefore, B's 1 day's work= 1/20 - 1/30 = 1/60

So, B alone could do the work in 60 days.