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, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

 A) 11 days B) 12 days C) 13 days D) 14 days

Explanation:

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10.

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.

Number of days required for this initial work = 7 days.

Thus, the total numbers of days required = 4 + 7 = 11 days.

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Q:

A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):

 A) 200, 250, 300 B) 300, 200, 250 C) 200, 300, 400 D) None of these

Explanation:

A's 5 days work = 50%

B's 5 days work = 33.33%

C's 2 days work = 16.66%     [100- (50+33.33)]

Ratio of contribution of work of A, B and C =  = 3 : 2 : 1

A's total share = Rs. 1500

B's total share = Rs. 1000

C's total share = Rs. 500

A's one day's earning = Rs.300

B's one day's earning = Rs.200

C's one day's earning = Rs.250

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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

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:

12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working  and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day?

 A) 8 B) 12 C) 16 D) 24

Explanation:

1 man's 1 day work =1/96 ; 1 woman's 1 day work = 1/192

Work done in 6 days=

Remaining work = 1/4

(8 men +8 women)'s 1 day work = $1896+8192$ =1/8

Remaining work =1/4 -  1/8 = 1/8

1/96 work is done in 1 day by 1 man

Therefore, 1/8 work will be done in 1 day by 96 x (1/8) =12 men

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Q:

An air conditioner can cool 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 = (a x b)/(a + b)

= (45 x 40)/(45 + 40)

= 45 x 40/85

= 21.1764

= 22 min (approx).

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Q:

Relation Between Efficiency and Time

A is twice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B.In how many days they can complee the whole work; working together?

Ratio of times taken by A and B = 1 : 2.

The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.

If difference of time is 1 day, B takes 2 days.

If difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/60

(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.

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Q:

A,B,C together can do a piece of work in 10 days.All the three started workingat it together and after 4 days,A left.Then,B and C together completed the work in 10 more days.In how many days can complete a work alone ?

 A) 25 B) 24 C) 23 D) 21

Explanation:

(A+B+C) do 1 work in 10 days.

So (A+B+C)'s 1 day work=1/10 and as they work together for 4 days so workdone by them in 4 days=4/10=2/5

Remaining work=1-2/5=3/5

(B+C) take 10 more days to complete 3/5 work. So( B+C)'s 1 day work=3/50

Now A'S 1 day work=(A+B+C)'s 1 day work - (B+C)'s 1 day work=1/10-3/50=1/25

A does 1/25 work in in 1 day

Therefore 1 work in 25 days.

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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.