# 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) 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.

**Sol : **In this kind of questions we find the work force required to complete the work in 1 day (or given unit of time) then we equate the work force to find the relationship between the efficiencies (or work rate) between the different workers.

Therefore, 6B+8G = 6 days

=> 6(6B+8G)= 1 day (inversely proportional)

=> 36B+48G =1 ( by unitary method)

Again 14B+10G = 4days

=> 56B+40G =1

so, here it is clear that either we employ 36B and 48G to finish the work in 1 day or 56B and 40G to finish the same job in 1 day. thus , we can say

=> 36B+48G = 56B+40G

=> G= 2.5B

Thus a Girl is 2.5 times as efficient as a boy.

Now, since 36B+48G = 1

=> 36B+48(2.5 B)=1

=>156B=1

i.e., to finish the job in 1 day 156 boys are required or the amount of work is 156 boys-days

Again 1G+1B=2.5B+1B=3.5B

Now, since 156 boys can finish the job in 1 day

so 1 boy can finish the job in 156 days

Therefore, 3.5 boys can finish the job in $\frac{1\times 156}{3.5}=\frac{4}{7}$ days.

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) 3 | B) 6 |

C) 9 | D) 12 |

Explanation:

The mother completes the job in x hours.

So, the daughter will take 2x hours to complete the same job.

In an hour, the mother will complete 1/x of the total job.

In an hour, the daughter will complete 1/2x of the total job.

So, if the mother and daughter work together, in an hour they will complete 1/x + 1/2x of the job.

i.e., in an hour they will complete 3/2x of the job.

The question states that they complete the entire task in 6 hours if they work together.

i.e., they complete 1/6 th of the task in an hour.

Equating the two information, we get 3/2x = 1/6

By solving for x, we get 2x = 18 or x = 9.

The mother takes 9 hours to complete the job.

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's 1 days work = 1/12

B's 1 days work =1/6

Therefore, (A+B)'s 1 day's work= 1/12 + 1/6 = 1/4

Therefore, Time taken by both to finish the whole work = $\frac{1}{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}$ = 4 days

**Alternatively :**

Efficiency of A =100/12 =8.33%

Efficiency of B =100/6=16.66%

Combined efficiency of A and B both = 8.33+16.66=25%

Therefore, Time taken by both to finish the work (working together) =100/25= 4days

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.

A) 10 2/3 days | B) 13 1/5 days |

C) 12 2/3 days | D) 11 5/7 days |

Explanation:

3/15 + 4/16 + x/24 = 1

$\Rightarrow x=13\frac{1}{5}$