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

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

$\inline \dpi{100} \fn_jvn Efficiency \propto \frac{1}{number\; of\; time\; units}$

$\inline \dpi{100} \fn_jvn \therefore Efficiency \times time=constant\; work$

Hence, $\inline \dpi{100} \fn_jvn Required \; time = \frac{work}{efficiency}$

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 = $\inline \fn_jvn \frac{100}{efficiency}$

Q:

Two pipes A and B can fill a tank in 24 hours and $17\frac{1}{7}$ hours respectively. Harihar opened the pipes A and B to fill an empty tank and some times later he closed the taps A and B , when the tank was supposed to be full. After that it was found that the tank was emptied in 2.5 hours because an outlet pipe "C" connected to the tank was open from the beginning. If Harihar closed the pipe C instead of closing pipes A and B the remaining tank would have been filled in :

 A) 2 hours B) 8 hours C) 6 hours D) 4 hours

Explanation:

Efficiency of Inlet pipe A = 4.16%       $\left(\frac{100}{24}\right)$

Efficiency of Inlet pipe B = 5.83%      $\left(\frac{100}{17\frac{1}{7}}\right)$

Therefore, Efficiency of A and B together = 100 %

Now, if the efficiency of outlet pipe be x% then in 10 hours the capacity of tank which will be filled = 10 *  (10 - x)

Now, since this amount of water is being emptied by 'C' at x% per hour, then

=> x = 8

Therefore, in 10 hours 20% tank is filled only. Hence, the remaining 80% of the  capacity will be filled by pipes A and B  in 80/10 = 8 hours

16 2065
Q:

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it ?

 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.

1 1987
Q:

Raghu can complete a work in 12days working 9 hours a day. Arun can complete the same work in 8 days working 11 hours a day. If both Raghu and Arun work together, working 12 hours a day, in how many days can they complete the work ?

A)

B)

C)

D)

 A) Option A B) Option B C) Option C D) Option D

Explanation:

Raghu can complete the work in (12 x 9)hrs = 108 hrs.

Arun can complete the work in (8 x 11)hrs = 88 hrs.

Raghu's 1 hrs work = 1/108 and Arun's 1 hrs work = 1/88

(Raghu + Arun)'s 1 hrs work = $\left(\frac{1}{108}+\frac{1}{88}\right)=\frac{49}{2376}$

So, both Raghu and Arun will finish the work in

Number of days of 12 hours each=$\left(\frac{2376}{49}×\frac{1}{12}\right)$ =

4 1901
Q:

3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 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.

2 1880
Q:

Twenty men can do a work in eighteen days. Eighteen women can complete the same work in fifteen days. What is the ratio between the capacity of a woman and a man ?

 A) 4:5 B) 3:4 C) 4:3 D) 2:3

Explanation:

(20 x 18) men can complete the work in in one day.

one man's one day work = 1/360

(18 x 15) women can complete the work in 1 day

1 woman's one day work = 1/270

So, required ratio = $\frac{1}{270}:\frac{1}{360}$= 4:3

10 1712
Q:

An air conditioner can coo the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room approximately ?

 A) 18 minutes B) 19 minutes C) 22 minutes D) 24 minutes

Explanation:

Let the two conditioners be A and B

'A' cools at 40min

'B' at 45min

Together =(axb)/(a+b) = (45x40)/85 = 21.1764 = (approx) 22 min.

1 1696
Q:

At Arihant Prakasham every book goes hrough 3 phases (or stages) typing, composing and binding. There are 16 typists, 10 composers and 15 binders. A typist can type 8 books in each hour, a composer can compose 12 books in each hour and a binder can bind 12 books in each hour. All of the people at Arihant Prakasham works for 10 hours a day and each person is trained to do only the ob of 1 category.How many books can be prepared in each day?

 A) 1500 B) 1200 C) 1440 D) 1380

Explanation:

T                 C              B

16              10             15

8                12             12

128            120           180             <------- in one hour

1280          1200         1800            <------- in 10 hours

Since, restriction is imposed by composers i.e,since only 1200 books can be composed i 10 hours so not more than 1200 books can be finally pepared.

3 1623
Q:

A contractor undertook to complete a piece of work in 120 Days and employed 140 men upon it. At the end of 66 days only half of the work was done,so he put on 25 extra men. By how much time did he exceed the specific time ?

 A) 2 days B) 3 days C) 4 days D) 5 days

Explanation:

work done=total number of person x number of days;
half of work done = 140 x 66;
For half of remaining work 25 extra men are added.
Therefore, total men for half work remaining = 140 + 25 = 165;
Let 2nd half work will be completed in K days;
140 x 66 = 165 x K
K = 122;
Hence, extra days => 122-120 = 2days.