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 Time and Work Questions

Popular Latest Rated Important Formulae

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 : 

Efficiency∝1No 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:

A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone  can finish the job?

A) 30 B) 40
C) 50 D) 60
 
Answer & Explanation Answer: B) 40

Explanation:

(A+B)'s 15 days work = 120×15=34

Remaining work =  1/4

Now, 1/4 work is done by A in 10 days.

Whole work will be done by A in (10 x 4) = 40 days.

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Q:

A and  B can do  a piece of work in 30 days , while  B and C can do the same work in 24 days and C and A in 20 days . They all work together for 10 days when B and C leave. How many days more will A take to finish  the work?

A) 18 days B) 24 days
C) 30 days D) 36 days
 
Answer & Explanation Answer: A) 18 days

Explanation:

2(A+B+C)'s 1 day work = 1/30 + 1/24 + 1/20 = 1/8

=>(A+B+C)'s  1 day's work= 1/16

work done by A,B and C in 10 days=10/16 = 5/8

Remaining work= 3/8

A's 1 day's work= 116-124=148

Now, 1/48 work is done by A in 1 day.

 So, 3/8 work  wil be done by A in =48 x (3/8) = 18 days

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Q:

A can finish a work in 15 days and B can do the same work in 12 days . B worked for 8 days and left the job .In how many days, A alone can finish the remaining work?

A) 6 days B) 5 days
C) 4 days D) 3 days
 
Answer & Explanation Answer: B) 5 days

Explanation:

B's 8 days work=(1/12) x 8 = 2/3

Reaining work= 1/3

Now, 1/15 work is done by A in 1 day

Therefore, 1/3 work is done by A in 15 x (1/3) = 5 days

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Q:

A works twice as fast as B.If  B can complete a work in 18 days independently,the number of days  in which A and B can together finish the work is:

A) 4 days B) 6 days
C) 8 days D) 10 days
 
Answer & Explanation Answer: B) 6 days

Explanation:

Ratio of rates of working of A and B =2:1. So, ratio of times taken =1:2

Therefore, A's 1 day's work=1/9 

B's 1 day's work=1/18 

(A+B)'s 1 day's work= 1/9 + 1/18 = 1/6

so, A and B together can finish the work in 6 days

 

 

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Q:

A can do a certain work in the same time in which B and C together can do it.If A and B together could do it in 20 days and C alone in 60 days ,then B alone could do it in:

A) 20days B) 40 days
C) 50 days D) 60 days
 
Answer & Explanation Answer: D) 60 days

Explanation:

(A+B)'s 1 day's work=1/20 

C's 1 day work=1/60 

(A+B+C)'s 1 day's work= 1/20 + 1/60 = 1/15

 

Also A's 1 day's work =(B+C)'s 1 day's work 

Therefore,  we get: 2 x (A's 1 day 's work)=1/15 

=>A's 1 day's work=1/30 

 

Therefore, B's 1 day's work= 1/20 - 1/30 = 1/60

So, B alone could do the work in 60 days.

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Q:

P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?

A) 60/11 B) 61/11
C) 71/11 D) 72/11
 
Answer & Explanation Answer: A) 60/11

Explanation:

P can complete the work in (12 x 8) hrs = 96 hrs 

Q can complete the work in (8 x 10) hrs=80 hrs 

Therefore, P's 1 hour work=1/96   and Q's 1 hour work= 1/80

(P+Q)'s 1 hour's work =(1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11 hrs  

Therefore, Number of days of 8 hours each = (480/11) x (1/8) = 60/11

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Q:

A, B and C can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:

A) 1/24 days B) 7/24 days
C) 24/7 days D) 4 days
 
Answer & Explanation Answer: C) 24/7 days

Explanation:

(A+B+C)'s 1 day's work = (1/24 + 1/6 + 1/12) = 7/24

so, A,B and C together will complete the work in 24/7 days.

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