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- Question
A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?
Options- A. 50
- B. 40
- C. 45
- D. 10
- Correct Answer
- 10
ExplanationLet the number of workers be x.
Now, Using work equivalence method,
X + (X-1) + (X-2)+ . . . . + 1 = X *55% of X
=> [X * (X+1)] / 2 = X * (55X/100) [because, Series is in AP. Sum of AP = {No. of terms (first term+ last term)/2} ]
Therefore, X = 10
- 1. The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:
Options- A. 4.5
- B. 5
- C. 6
- D. 9 1/3 Discuss
- 2. 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 ?
Options- A. 25
- B. 24
- C. 23
- D. 21 Discuss
- 3. A Contractor employed a certain number of workers to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?
Options- A. 10 %
- B. 14 ( 2/7 )%
- C. 20 %
- D. Can't be determined Discuss
- 4. 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:
Options- A. 4 days
- B. 6 days
- C. 8 days
- D. 10 days Discuss
- 5. 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:
Options- A. 20days
- B. 40 days
- C. 50 days
- D. 60 days Discuss
- 6. (x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?
Options- A. 27 days
- B. 12 days
- C. 25 days
- D. 18 days Discuss
- 7. 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 ?
Options- A. 18 minutes
- B. 19 minutes
- C. 22 minutes
- D. 24 minutes Discuss
- 8. 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 ?
Options- A. 6
- B. 9
- C. 5
- D. 7 Discuss
- 9. 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:
Options- A. 12 days
- B. 18 days
- C. 24 days
- D. 30 days Discuss
- 10. A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C, when they work individually?
Options- A. 2:6:3
- B. 2:3:6
- C. 1:2:3
- D. 3:1:2 Discuss
Time and Work problems
Search Results
Correct Answer: 6
Explanation:
A : C
Efficiency 5 : 3
No of days 3x : 5x
Given that, 5x-6 =3x => x = 3
Number of days taken by A = 9
Number of days taken by C = 15
B : C
Days 2 : 3
Therefore, Number of days taken by B = 10
Work done by B and C in initial 2 days = = 1/3
Thus, Rest work =2/3
Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days
Correct Answer: 25
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.
Correct Answer: 14 ( 2/7 )%
Explanation:
Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.
D * x +(100- D) * 2x= 175x
=> D= 25 days
Now , the work done in 25 days = 25x
Total work = 175x
Therefore, workdone before increasing the no of workers = % =
Correct Answer: 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
Correct Answer: 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.
Correct Answer: 12 days
Explanation:
=> x= 20 and x=-14
so, the acceptable values is x=20
Therefore, Total work =(x-2)x = 18 x 20 =360 unit
Now 360 = 30 x k
=> k=12 days
Correct Answer: 22 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).
Correct Answer: 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.
Correct Answer: 18 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
Correct Answer: 2:6:3
Explanation:
A : B : C
Ratio of efficiency 3 : 1 : 2
Ratio of No.of days 1/3 : 1/1 : 1/2
or 2 : 6 : 3
Hence A is correct.
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