Question

if 38 men, working 6 hours a day, can do a piece of work in 12days, find the number of days in which 57 men, working 8 hours a day, can do twice that piece of work. Suppose that 2 men of the first set do as much work in one hour as 3 men of the second set do in 1.5hours.
A) 36
B) 32
C) 39
D) 27​

Answer 1

Answer:

27

Step-by-step explanation:

Given If 38 men, working 6 hours a day, can do a piece of work in 12 days, find the number of days in which 57 men, working 8 hours a day, can do twice that piece of work. Suppose that 2 men of the first set do as much work in one hour as 3 men of the second set do in 1.5 hours.

Number of men, days, number of work and number of hours per day are for first group to complete the work along with number of men, work and number of hours per day for the double amount of work and number of days required for second group of men.

Let efficiency of men of first group = E1 and that of men of second group be E2

So we have

M1 x D1 x H1 X E1 X W2 = M2 X D2 X H2 X E2 X W1

WE know that

M1 = 38 D1 = 12 H1 = 6  W1 = 1

W2 = 2 M2 = 57 D2 = ? H2 = 8  

Now work done by 2 men of first group in 1 hour = work done by 3 men of second group in 1.5 hours. Men and efficiency are inversely proportional to each other.

So E1 : E2 = 3 x 1.5 : 2 x 1 = 4.5 : 2

E1 = 4.5 and E2 = 2

Substituting in the above formula we get

38 x 12 x 6 x 4.5 x 2 = 57 x D2 x 8 x 2 x 1

24624 = 912 D2

D2 = 27 days

Therefore number of days will be 27 days

Answer 2

Answer:

27

Step-by-step explanation:

Men and hours are inversely proportional to each other, but their product is  directly proportional to the work done.

Considering workers of set 1,

Men        Hours              Work done

38      72(12 days*6)                1

1               38*72                       1

2               19*72                       1

2                   1                        1/19*72      ....(i)

Considering workers of set 2,

Men        Hours              Work done

57       8b(b days*8)                2

1                57*8b                     2

3               19*8b                      2

3                   1                      2/19*8b

3                  3/2              $\frac{3}{2}$*$\frac{2}{19*8b}$ = 3/19*8b      .....(ii)

In accordance with the question, we are equating (i) and (ii),

$\frac{1}{19*72}$ = $\frac{3}{19*8b}$

Upon cross multiplying we get,

19*8b = 3*19*72

8b = 3*9*8

b = 27

And that's how I got this answer. I wanted to share it here, as this is my own method of solving this sum and I solemnly do hope that many of my peers do benefit from this. Thank You!