# 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 :

Hence,

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 = $\frac{100}{Efficiency}$

Q:

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:

 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

7 5509
Q:

A contractor undertakes to complete a work in 130 days. He employs 150 men for 25 days and they complete 1/4 of the work . He then reduces the number of men to 100, who work for 60 days, after which there are 10 days holidays.How many men must be employed for the remaining period to finish the work?

150 men in 25 days do = $\frac{1}{4}$ work

Let 1 man in 1 day does = x  work

Total work done by 150 men in 25 days = 150x *  25 = $\frac{1}{4}$   work => x = $\frac{1}{15000}$

Therefore, 100 men in 60 days do = 100 * 60x = 6000x work = 6/15 = 2/5

Total work done =

Therefore, Remaining work = 1 - $\frac{13}{20}$ = $\frac{7}{20}$

Remaining time = 130 - (25+60+10) = 35 days

Therefore, work is done in 25 days by 150 men.

Therefore, Work is done in 35 days by 150 men.

Hence, he should employ 50 more men.

5442
Q:

A and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

(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 = $22×\frac{9}{200}=\frac{198}{200}$

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 $40×\frac{1}{100}=\frac{2}{5}$

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

5134
Q:

4 men can repair a road in 7 hours. How many men are required to repair the road in 2 hours ?

 A) 17 men B) 14 men C) 13 men D) 16 men

Explanation:

M x T / W = Constant
where, M= Men (no. of men)
T= Time taken
So, here we apply
M1 x T1/ W1 = M2 x T2 / W2
Given that, M1 = 4 men, T1 = 7 hours ; T2 = 2 hours, we have to find M2 =?
Note that here, W1 = W2 = 1 road, ie. equal work load.
Clearly, substituting in the above equation we get, M2 = 14 men.

3 4950
Q:

When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. who is most efficient?

 A) A B) B C) C D) can't be determined

Explanation:

A + B= 70%

B + C =50%

=> B= 20%     A= 50%        and   C=30%

Hence A is most efficient

11 4757
Q:

Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?

 A) 4:18 pm B) 3:09 pm C) 12:15 pm D) 11:09 am

Explanation:

Efficiency of P= 100/20= 5% per hour

Efficiency of Q= 100/25= 4% per hour

Efficiency of R= 100/40= 2.5% per hour

Efficiency of S=100/50= 2% per hour

Cistern filled till 10 am by P, Q and R

Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern.

Rest of cistern to be filled = 100 - 30.5 = 69.5%

Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern

= 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx).

Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins

It means cistern will be filled up at 3:09 pm

6 4718
Q:

A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 40 days, then together ,all will finish the work in  ?

 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.

12 4388
Q:

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days  ?

 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.