Aptitude Time and Work Test Paper 6

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

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.

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

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

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.