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 =1n

2. If A’s 1 day's work =1n, 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 : 

Efficiency1No of time units

 

 Efficiency × Time = Constant Work

 

Hence, Required time = WorkEfficiency

 

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 = 100Efficiency

Q:

X can complete the work in 10 days, Y can do the same in 15 days. If they are hired for 5 days to do the work together, what is the work that left unfinished?

A) 1/3 B) 2/3
C) 1/6 D) 5/6
 
Answer & Explanation Answer: C) 1/6

Explanation:

Given X can do in 10 days 

=> 1 day work of X = 1/10

 

Y can do in 15 days 

=> 1 day work of Y = 1/15

 

1day work of (X + Y) = 1/10 + 1/15 = 1/6

 

Given they are hired for 5 days

 => 5 days work of (X + Y) = 5 x 1/6 = 5/6

 Therefore, Unfinished work = 1 - 5/6 = 1/6 

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11 9064
Q:

K can build a wall in 30 days. L can demolish that wall in 60 days. If K and L work on alternate days, when will the wall be completed ?

A) 120 days B) 119 days
C) 118 days D) 117 days
 
Answer & Explanation Answer: D) 117 days

Explanation:

K's work in a day(1st day) = 1/30
L's work in a day(2nd day)= -1/60(demolishing)
hence in 2 days, combined work= 1/30 - 1/60 =1/60
since both works alternatively, K will work in odd days and L will work in even days.
1/60 unit work is done in 2 days
58/60 unit work will be done in 2 x 58 days = 116 days
Remaining work = 1-58/60 = 1/30
Next day, it will be K's turn and K will finish the remaining 1/30 work.
hence total days = 116 + 1 = 117.

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13 9043
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
 
Answer & Explanation Answer: A) 2 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.

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12 8973
Q:

5 men and 3 boys can together cultivate a 23 acre field in 4 days and 3 men and 2 boys together can cultivate a 7 acre field in 2 days. How many boys will be needed together with 7 men, if they cultivate 45 acre of field in 6 days.

A) 6 B) 4
C) 2 D) 3
 
Answer & Explanation Answer: C) 2

Explanation:

Let work done by 1 man in i day be m

and Let work done by 1 boy in 1 day be b

From the given data,

4(5m + 3b) = 23

20m + 12b = 23....(1)

2(3m + 2b) = 7

6m + 4b = 7 ....(2)

By solving (1) & (2), we get

m = 1, b = 1/4

Let the number of required boys = n

6(7 1 + n x 1/4) = 45

=> n = 2.

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6 8971
Q:

The ratio of efficiencies of P, Q and R is 2 : 3 : 4. While P and R work on alternate days and Q work for all days. Now the work completed in total 10 days and the total amount they get is Rs. 1200. Find the amount of each person(respectively).

A) 200, 600, 400 B) 400, 600, 200
C) 600, 200, 400 D) 400, 200, 600
 
Answer & Explanation Answer: A) 200, 600, 400

Explanation:

Ratio of efficiencies of P, Q and R = 2 : 3 : 4

From the given data,

Number of working days of P, Q, R = 5 : 10 : 5

Hence, ratio of amount of p, Q, R = 2x5 : 3x10 : 4x5 = 10 : 30 : 20

Amounts of P, Q, R = 200, 600 and 400.

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8 8870
Q:

P alone can do a piece of work in 24 days. The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work. How many days are required to complete by P and Q working together ?

A) 9 3/5 days B) 7 days
C) 6 3/7 days D) 8 days
 
Answer & Explanation Answer: A) 9 3/5 days

Explanation:

Let the total work be 'W'

As per the given information,

P can complete the work 'W' in 24 days.

=> one day work of P = W/24

And also given that,

The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work

=> PW/3 = QW/2

=> P's

1 day =    W/24

   ?    =      W/3

=>  ?  = 24W/3W  = 8

=> QW/2 = 8 days

=> Q alone can complete the work W in 16 days

=> P + Q can complete the work in

1/24 + 1/16 = 5/48

=> 48/5 days = 9 3/5 days.

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18 8840
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
 
Answer & Explanation Answer: C) 4:3

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 = 1270:1360= 4:3

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13 8831
Q:

A is 50% more efficient than B. They together start the work and 7/12th of work is left after 8 days. Find in what time B alone will complete the whole work.

A) 36 days  B) 44 days 
C) 50 days  D) 40 days 
 
Answer & Explanation Answer:

Explanation:

Ratio of efficiency of A to B is 3 : 2

Let, In 8 days they complete = (3 + 2) × 8 = 40 units

So, total work = 40 × 12/5 units

Time taken by B alone to complete whole work = 40 ×  12/5 ×2 = 48 days 

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5 8778