# 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) 50 days | B) 48 days |

C) 47.5 days | D) 49 days |

Explanation:

50 men can build a tank in 40 days

Assume 1 man does 1 unit of work in 1 day

Then the total work is 50×40 = 2000 units

50 men work in the first 10 days and completes 50×10 = 500 units of work

45 men work in the next 10 days and completes 45×10 = 450 units of work

40 men work in the next 10 days and completes 40×10 = 400 units of work

35 men work in the next 10 days and completes 35×10 = 350 units of work

So far 500 + 450 + 400 + 350 = 1700 units of work is completed and

Remaining work is 2000 - 1700 = 300 units

30 men work in the next 10 days. In each day, they does 30 units of work.

Therefore, additional days required = 300/30 =10

Thus, total 10+10+10+10+10 = 50 days required.

A) 38 | B) 72 |

C) 36 | D) 76 |

Explanation:

Given 4men, 12 women and 20 children work for 2 days.

Workdone for 2 days by 4men, 12 women and 20 children = $\frac{\mathbf{4}\mathbf{}\mathbf{x}\mathbf{}\mathbf{2}}{\mathbf{6}\mathbf{}\mathbf{x}\mathbf{}\mathbf{12}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{12}\mathbf{}\mathbf{x}\mathbf{}\mathbf{2}}{\mathbf{8}\mathbf{}\mathbf{x}\mathbf{}\mathbf{18}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{20}\mathbf{}\mathbf{x}\mathbf{}\mathbf{2}}{\mathbf{18}\mathbf{}\mathbf{x}\mathbf{}\mathbf{10}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\mathbf{2}}$

Therefore, remaining work = 1 - $\frac{1}{2}$ = $\frac{1}{2}$

To complete the same work by only men in 1 day,

We know that M1 x D1 = M2 x D2

Here M1 = 6 , D1 = 12 and M2 = M , D2 = 1

12 x 6 = M x 1

=> M = 12 x 6 = 72

=> But the remaining work = 1/2

Men required => 1/2 x 72 = 36

Only men required to Complete the remaining work in 1 day = 36.

A) 87.5 | B) 89 |

C) 91.5 | D) 93.5 |

Explanation:

We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)

(60 x 30 x 8)/ 150 = (35 x D2 x 6) / 200

D2 = (60 x 30 x 8 x 200) / (150 x 35 x 6) => D2 = 91.42 days =~ 91.5 days.

A) 24 $ | B) 22 $ |

C) 16 $ | D) 14 $ |

Explanation:

Let the 1 day work of a boy=b and a girl=g, then

2b + g = 1/5 ---(i) and

b + 2g = 1/6 ---(ii)

On solving (i) & (ii), b=7/90, g=2/45

As payment of work will be in proportion to capacity of work and a boy is paid $ 28/week,

so a girl will be paid $28\times \frac{{\displaystyle \frac{2}{45}}}{{\displaystyle \frac{7}{90}}}$ = 16 $.

A) 145 | B) 165 |

C) 175 | D) 135 |

Explanation:

Given that,

working days = 5

working hours = 8

A man get rupess per hour is Rs.2.40

So in one day the man get total rupees is 2.40 x 8 = 19.2

So in 5 days week the man get total rupees is 19.2 x 5 = 96

So in 4 week the man get total rupees is 96 x 4 = 384

So the man worked for = 160hours in 4 weeks

But given that the man earned Rs.432

Hence remaning money is (432-384 = 48)which is earn by doing overtime work

Overtime hours = 48/3.20 = 15

So total worked hours is = 15 + 160 = 175.

A) 12 days | B) 24 days |

C) 32 days | D) 16 days |

Explanation:

It is given that efficiency ratio =3:1

so time ratio will be 1:3 (since work is same)

Also given that time diff = 32 days. ratio difference = 3-1 =2

2 ratio = 32 days

1 ratio = 16 days.

So A will alone finish it in 16 days and B will finish it in 16*3 = 48 days.

Total work = LCM of 16 and 48 = 48.

Total time = Total work/Total efficiency

ie; 48/4= 12 days.

A) 36 | B) 32 |

C) 22 | D) 28 |

Explanation:

Let the total women in the group be **'W'**

Then according to the given data,

**W x 20 = (W-12) x 32**

=> W = 32

*Therefore, the total number of women in the group =* 32

A) 16 days | B) 13 days |

C) 15 days | D) 12 days |

Explanation:

Ratio of times taken by P & Q = 100 : 130 = 10:13

Let Q takes x days to do the work

Then, 10:13 :: 23:x

=> x = 23x13/10

=> x = 299/10

P's 1 day's work = 1/23

Q's 1 day's work = 10/299

(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Hence, P & Q together can complete the work in **13** days.