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:

P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together  ?

A) 5 (2/3) B) 6 (3/4 )
C) 4 (1/2) D) 3
 
Answer & Explanation Answer: C) 4 (1/2)

Explanation:

Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total. 

 

Work done by P and Q, working together in one day = 1/6 + 1/18  = 4/18 = 2/9 

 

They would take 9/2 days = 4 (1/2) days to complete the work working together.

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

9 11085
Q:

Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work  ?

A) 18 days B) 20 days
C) 16 days D) 14 days
 
Answer & Explanation Answer: B) 20 days

Explanation:

(5m + 9w)10 = (6m + 12w)8 

=> 50m + 90w = 48w + 96 w    => 1m = 3w

5m + 9w = 5m + 3m = 8m

 

8 men can do the work in 10 days.

3m +3w = 3m + 1w = 4m

So, 4 men can do the work in (10 x 8)/4 = 20 days.

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

9 12799
Q:

Raghu can do a job in 12 days alone and Sam can do the same job in 15 days alone. A third person Aru whose efficiency is two-third of efficiency of both Ram and Shyam together, can do the same job in how many days alone?

A) 10 B) 12
C) 13 D) 15
 
Answer & Explanation Answer: A) 10

Explanation:

One day work of Raghu and Sam together = 1/12 + 1/15 = 9/60 = 3/20

Aru efficiency = 2/3 of (Raghu + Sam)

Number of days required for Aru to do thw work alone = 3/2 x 20/3 = 10 days. 

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Analyst , Bank Clerk , Bank PO

9 4700
Q:

Meghana alone would take 32 hours more to complete a job than both Meghana and Ganesh together. If Ganesh worked alone, he took 12 1/2 hours more to complete it than both Meghana and Ganesh worked together. What time would they take if both Meghana and Ganesh worked together?

A) 20 hrs B) 18 hrs
C) 22 hrs D) 20.5 hrs
 
Answer & Explanation Answer: A) 20 hrs

Explanation:

Time taken by both Meghana and Ganesh to work together is given by =

t1 x t2 

Where

t1 = 32 hrst2 = 12 12 hrs = 252 hrs

 

Therefore, time took by both to work together = 

32 x 252 = 16 x 25 = 4 x 5 = 20 hrs

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Analyst , Bank Clerk , Bank PO

9 3629
Q:

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

A) 4 B) 3
C) 2 D) 1
 
Answer & Explanation Answer: C) 2

Explanation:

Let workdone 1 boy in 1 day be b

and that of 1 girl be g

From the given data,

4(5b + 3g) = 23

20b + 12g = 23 .......(a)

 

2(3b + 2g) = 7

6b + 4g = 7 ........(b)

 

Solving (a) & (b), we get

b = 1, g = 1/4

 

Let number og girls required be 'p'

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

=> p = 2.

 

Hence, number of girls required = 2

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Analyst , Bank Clerk , Bank PO

9 2405
Q:

9 girls working 7 hours a day can complete a piece of work in 15 day. In how many days can 6 girls working for 9 hours a day, complete the same piece of work?

A) 35/4 days B) 17.5 days
C) 19 3/4 days D) 37/3 days
 
Answer & Explanation Answer: B) 17.5 days

Explanation:

Let the number of days be 'p' 

As the work is same, we know that

M1 x D1 x H1 = M2 x D2 x H2

Where M = Men, D = Days, H = Hours per day 

Here M1 = 9, D1 = 15, H1 = 7 

M2 = 6, D2 = p, H2 = 9 

=> 9 x 15 x 7 = 6 x p x 9 

=> p = 35/2 = 17.5 days.

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk , Analyst

8 3349
Q:

Two persons Shyam and Rahim can do a job in 32 days together. Rahim can do the same job in 48 days alone. They started working together and after working 8 days Rahim is replaced by a third person Ram whose efficiency is half that of Rahim. Find in how many days the remaining work will be completed by both Shyam and Ram together?

A) 16 days B) 72/5 days
C) 15 days D) 96/5 days
 
Answer & Explanation Answer: B) 72/5 days

Explanation:

Work done by Shyam and Rahim in 8 days = 8/32 = 1/4

Remaining work to be done by Shyam and Ram = 1 - 1/4 = 3/4

Given efficieny of Ram is half of Rahim i.e, as Rahim can do the work in 48 days, Ram can do the work in 24 days.

One day work of Ram and Shyam = (1/32 - 1/48) + 1/24 = 5/96

Hence, the total work can be done by Shyam and Ram together in 96/5 days.

 

Therefore, remaining work 3/4 can be done by them in 3/4 x 96/5 = 72/5 = 14.4 days.

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Analyst , Bank Clerk , Bank PO , IT Trainer

8 5472
Q:

In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap. If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of  efficiency of 8th tap and 12th tap, respectively?

A) 4:1 B) 5:3
C) 16:1 D) 1:16
 
Answer & Explanation Answer: D) 1:16

Explanation:

Time taken by 8th tap = 2 x 2 x 2= 8 hours

Time taken by 12th tap = 2x (1/2) x (1/2)  = 1/2 hour

Ratio of time taken by 8th tap and 12th tap = 8 : 1/2 =16:1

Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16

Report Error

View Answer Report Error Discuss

Filed Under: Time and Work

8 5392