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Aptitude Time and Work Test Paper 7


31) A, B, and C together can complete a work in 6 days. The efficiency of A and C is 3 times of B, and the efficiency of A is 4 times of C, and then they alone can finish the job in how many days.

  1. 10, 24, 40 days
  2. 15, 30, 60 days
  3. 12, 12, 18 days
  4. 15, 60, 30 days

Answer: A

Explanation:

ATQ, (A+B+C) can finish a work in 6 days

The efficiency of (A+C): B = 3: 1

Then total work = Efficiency * total days
i.e., total work = (3+1) * 6 = 24
So, B can finish the work in, work/efficiency = 24/1 = 24 days
And, (A+B) can finish a work in 24/3 = 8 days..................................... (i)

Now, Efficiency of A: C= 4: 1
According to equation 1
(A+C) together can finish the work in 8 days

The total work, in this case, = Efficiency of (A and C) * days
i.e., total work = 8 * 5 = 40 unit
Hence, A can finish the work in 40/4 = 10 days
C can finish the work in 40/1 = 40 days


32) A does half as much as work as B in 1/6 of the time taken by B. Together they can complete the work in 10 days. B alone can complete the work in how many days?

  1. 20 days
  2. 30 days
  3. 40 days
  4. 50 days

Answer: C

Explanation:

Let B does 1 work in x days
Then, A does [1/2] work in x/6 days
To do 1 unit work, A will take x/3 days

That means time ratio of A: B = x: x/3
Or time ratio = 1: 1/3
Or time ratio = 3: 1

As we know that the efficiency ratio is inversely proportional to time ratio

i.e., Efficiency ratio of A: B = 1: 3

ATQ,

(A+B) = 10 days
Total work = days* efficiency of (A+B)
Or, total work = 10 * 4 = 40 units
i.e., B can finish the work in = total work/ efficiency of B

So, B can finish the work in 40/1 = 40 days.


33) A man can finish a work in 20 days, a woman can finish the same work in 30 days, and a boy can finish the same work in 60 days. 2 men, 8 women, and some boys working together can finish the work in 2 days. Find how many boys are working?

  1. 10 boys
  2. 8 boys
  3. 9 boys
  4. 15 boys

Answer: B

Explanation:

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

Take the LCM of days = LCM of (20, 30, and 60) = 60
Let the total work = 60

1 Man's one day work = 60/20 = 3 unit
1 Woman's one day work = 60/30 = 2 unit
1 The boy's one day work = 60/60 = 1 unit........................ (i)

ATQ, (2Men + 8Women + x Boy) can finish a work in 2 days.

Or, (2Men + 8women)'s 1 day work = 2 * 3 + 8*2 = 22

Or, (2Men + 8women)'s 2 day work = 22* 2 = 44
Remaining work = 60- 44 = 16
That means remaining 16 work is done by X boys in 2 days
Or, X boys' one day work = 16/2 = 8

By equation 1, 1 boy completes 1 unit work per day
So, 8 boys are required to complete 8 units of work per day.


34) A contractor undertakes to complete the job in 38 days. He assigns 30 workers on the job, and after 25 days he assigns 5 more workers and finishes the work one day before the given time. If he did not assign extra numbers of workers then work will be late by how many days.

  1. 1 day
  2. 2 days
  3. 5 days
  4. 1.5 days

Answer: A

Explanation:

ATQ, target = work should be finished in 38 days

Now, after assigning more workers, the work is finished in 37 days.

Note: man * days = total work

As per the given information,
Total work = (30 Men * 25 days) + (35 men * 12 days) = 30*25 + 35*12
Or, total work = 750 + 420 = 1170

Note: 1 worker = 1 unit work per day

So, if work is done by 30 workers, i.e., 30 units of work per day
The number of days required = total work/ work per day
                                = 1170/30= 39 days

Target with 30 workers = 38, but it will take 39 days
So, work will be late by 1 day.


35) 30 men can complete the work in 30 days. If after every 10 days, 5 workers leave the job, the work will be finished in how many days?

  1. 32 days
  2. 35 days
  3. 37 days
  4. 40 days

Answer: D

Explanation:

Men = 30, days = 30

Total work = men * days = 30*30 = 900 units of work

ATQ,

1st 10 days work done = Men * days = 30*10= 300................ (i)
Next 10 days work done = Men * days = 25 * 10= 250.......... (ii)
Next 10 days work done = Men * days = 20 * 10 = 200......... (iii)
Next 10 days work done = Men * days = 15 * 10 = 150.......... (iv)

The total work done in 40 days = 300+ 250+ 200+ 150 = 900 units

ATQ, the total work which is 900 units should be completed in 30 days, but according to the solution, it takes 10 more days to get completed.

So, the work will be completed in 40 days.



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