Time and Work Test - 2

A pit can be dug by 4 men in 16 days.
Therefore, a pit can be dug by 1 man in 64 days.
Each man does 1/64 of the work in 1 day.
Now, work done by 8 men in one day = 8/64 = 1/8
Thus, 8 men can do the work in 8 days.

Let work done by 1 man in 1 day = m
Let total amount of work = 6W

As in 11 days, only 1/6^th of the work is done, we have 48 x m x 11 = W
Or m = W/(11 x 48) ... (i)

Let n men be employed to complete the rest of the work (6W - W = 5W) in 44 (55 -11 = 44) days.
So, n x m x 44 = 5W ... (ii)

Putting the value of m from equation (i) into equation (ii) and solving for n, we get n = 60

Thus, number of more men to be employed = 60 - 48 = 12

3 hours = 3 x 60 minutes = 180 minutes
In 180 minutes he examines 5 patients with 4 breaks of 10 minutes each between 2 consecutive patients.

Thus, time taken for examining 1 patient = ((180 - 40)/5) minutes = 28 minutes
10 hours 15 minutes = (10 x 60 + 15 = 615) minutes

If he examines n patients in a day, then he has (n - 1) break periods of 10 minutes
So, 28n + 10(n - 1) = 615.

Or, n = 16.447
But, the number of patients has to be integral.

So, n = 16 or 17
Time taken to examine 16 patients = (28 x 16 + 10 x 15) minutes = 598 minutes

Thus, after examining 16 patients, he is left with (615 - 598 = 17) minutes.

As he needs 28 minute to examine 1 patient, he cannot examine another patient after having examined 16 patients.

Hence, he examines 16 patients.

A can do 1/6 of the work in one day and B can do 1/8 of the work in one day.
Together, they can do 1/6 + 1/8 = 7/24 work in one day.

Therefore, together they can complete the work in 24/7 days.
Hence, the total number of days it will take them to complete twice the same work = 48/7.

One man = 1.5 boys
∴ 6 boys = 4 men

⇒ 12 men (8 men + 6 boys = 12 men) can complete the work in 15 × 4/12 = 5 days.

et A, B and C take x, y and z days, respectively.
1/x + 1/y = 1/30 ………(1)
1/y + 1/z = 1/24 ………(2)
1/z + 1/x = 1/20 ...…....(3)

Solving these equations simultaneously, we get
1/x + 1/y + 1/z = 1/16 ...…….(4)

By solving (2) and (4), we get x = 48.
A, B and C together complete a job in 16 days.

In ten days, 10/16 of the job is completed and 6/16 of the job remains.
∵ x = 48, i.e. A completes 1/48 of the job in one day.

∴ A completes 6/16 of job in (6/16) 48 = 18 days