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Aptitude Time and Work Test Paper 6


26) A can finish a work in 8 hours, B can finish the same work in 12 hours, and C can do it in 24 hours. All the three starts work at 3 am, 4 am, and 5 am respectively. At what time work will be completed?

  1. 6 am
  2. 7: 40 am
  3. 8 am
  4. 5 am

Answer: B

Explanation:

Note: Assume the total work = LCM of the given time

Take the LCM of hours = LCM of (8, 12, and 24) = 24
Let the total work = 24

Note: One hour work = (total work/ time)

Now,

A's one hour work = 24/8 = 3 unit
B's one hour work = 24/12 = 2 unit
C's one hour work = 24/24= 1 unit

ATQ, between 3 am - 4 am, A works alone and finish 3 units of work
Between 4 am - 5 am, A and B work and complete 3+2 = 5 units of work
Between 5 am - 6 am, A, B, and C works and finishes 3+2+1 = 6 units of work

Or, between 3 am to 5 am, 8 unit of work is finished.
Remaining 24-8= 16 unit (till 5am)
After 5 am, A+B+C work together and finish 6 unit of work per hours.

i.e., 6 unit work = 1 hour

To complete the 16 unit work, multiply both sides with 2

i.e., 12 unit work = 2 hours
Remaining work = 16-12 = 4 unit work

As we know, 6 work = 1 hour
Or, 1 work = 1/6 hours
Or, 4 work = 4/6 or 2/3 hours.

That means (2 + 2/3) hours requires after 5 am.

So, time taken to complete the work is (5 +2 + 2/3) = 7:40am


27) A and B work separately in 15 hours and 12 hours respectively. Another man C can destroy the work in 4 hours. If they start doing work at 8 am, 9 am, and 11 am respectively. At what time the total work will be destroyed?

  1. 11 am
  2. 12 pm
  3. 2:40 pm
  4. 3:20pm

Answer: C

Explanation:

Note: Assume the total work = LCM of the given time

Take the LCM of hours = LCM of (15, 12, and 4) = 60
Let the total work = 60

Note: One hour work = (total work/ time)

Now,

A's one hour work = 60/15 = 4 unit
B's one hour work = 60/12 = 5 unit
C's one hour work = 60/4= 15 unit

ATQ, between 8 am - 9 am, A works alone and finish 4 units of work
Between 9 am - 10 am, A and B work and complete 4+5 = 9 units of work
Between 10 am - 11 am, A and B work and complete 4+5 = 9 units of work
Between 11 am - 12 am, A, B works, and C destroys it. i.e., 4+5 - 9 = - 6 unit of work
Where -ve indicates destroyed work
That means after 11 am, the net work is -6 per hour.
Total work till 11 am = 4+9+9= 22 unit

Destroy 6 unit works in 1 hour, or 1 unit work in 1/6 hours.
Time taken to destroy 22 unit works = 22/6 = 11/3 hours
Or, 3[2/3] hours

Hence, at 11am + 3[2/3] hours = 2:40 pm the total work will be destroyed.


28) A can complete a wall in 30 hours. B uses 30 bricks per hour, and together they can finish the wall in 12 hours. How many bricks are in the wall?

  1. 800 bricks
  2. 600 bricks
  3. 620 bricks
  4. 500 bricks

Answer: B

Explanation:

Note: Assume the total work = LCM of the given time

Take the LCM of hours = LCM of (30 and 12) = 60
Let the total work = 60

Note: One hour work = (total work/ time)

A's one hour work = 60/30 = 2 unit
(A+B)'s one hour work = 60/12 = 5 unit
B's one hour work = 2+B = 5 units, or, B = 3 units

B alone can complete the work in 60/3 = 20 hours
And, B uses 30 bricks per hour.

Hence, total bricks in the wall = 20*30 = 600 bricks


29) A and B can complete a wall in 15 and 20 hours respectively. If they work together, the wall is completed in 12 hours and they use 280 less bricks. Find the total number of bricks in the wall.

  1. 8400 bricks
  2. 16800 bricks
  3. 10000 bricks
  4. 12000 bricks

Answer: A

Explanation:

Note: Assume the total work = LCM of the given time

Take the LCM of hours = LCM of (15 and 20) = 60
Let the total bricks = 60

Note: One hour work = (total work/ time)

A's one hour work = 60/15 = 4 bricks
B's one hour work = 60/20 = 3 bricks

(A+B)'s one hour work = 4+3 = 7 bricks....................... (i)
But, ATQ
(A+B)'s one hour work = 60/12 = 5 bricks.................... (ii)

The difference between equation i and ii = 2 bricks/hour
But, ATQ it is 280 bricks
i.e., multiple of 140
So, multiply the total work with 140
Hence, 60* 140 = 8400 bricks


30) The efficiency ratio of A, B, and C are 2:3:4. To finish a job A takes 10 days more than B, if they work together, the work will be completed in how many days?

  1. 6[2/3] days
  2. 10 days
  3. 15 days
  4. 18 days

Answer: A

Explanation:

Note:
(i) Efficiency and time are inversely proportional to each other.
(ii) If 3 efficiencies are given, we have to calculate the time ratio and then reciprocate each efficiency and multiply with the LCM of given efficiencies.
(iii) Efficiency * total days = total work

ATQ,

Efficiency of A: B: C =2: 3: 4
Calculate the LCM of (2, 3, and 4) = 12
Now, reciprocate the efficiencies = ½: 1/3: ¼
Multiply each with 12 and we get time ratio
Time ratio of A: B: C = 12 *[1/2]: 12*[1/3]: 12*[1/4] = 6: 4: 3

The difference between A and B's time ratio = 2, but ATQ, it is 10
i.e., to calculate the days multiply time ratio with 5, then we get 6*5: 4*5: 5*3
The ratio of days= 30: 20: 15
Total work = efficiency * days = 30 * 2= 60, or 20*3= 60, or 15*4= 60
If all three work together
i.e., (A+B+C)'s one day work = 2+3+4 = 9
Or, days required = total work/ (A+B+C)'s one day work
Or, 60/9 = 20/3 = 6[2/3] days
Hence, 6[2/3] days are required to complete the work.



Aptitude Time and Work Test Paper 1
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Time and Work Concepts





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