Time and work Concept of MAN-DAY-HOUR with solved examples

 Concept of Man - Work - Hour  Formula

1.More men can do more work.

2.More work means more time required to do work.

3.More men can do the same work in less time.

4.If M1 can do W1 work in D1 days working H1 hr/day for Rs. R1 and for same work If M2 can do W2 work in D2  days working H2 hr/day for Rs. R2

Then,

(M D H)/(WR) = Constant

(M1 D1 H1)/(W1 R1) = (M2 D2 H2)/(W2 R2)

Solved examples Based on the MAN-DAY-HOUR formula.

Ex.1 If 24 men can complete in 8 days when they were 6 hours then how many days 36 men complete half work. If they work 12 hours per day.

Sol. (24*8*6)/1 = (36*D2*12)/(1/2)

(24*8*9) = 36* D2*24

D2 = 11/3 Ans.

Ex.2 24 men 16 days they started the work after 4 days 6 men left the work. then find in how many days they finished the remaining work.

Sol. MAN- DAY is Constant

 Therefore we get the equation

 

24*16 = 24*4 +16D

D = 18 Ans.

Ex.3 36 men can do a work in 16 days they started the work together after 4 days 6 men left and 48 women joined them then how many days remaining work will be completed if men do twice.

Sol. 36M * 16 = 36M *4 + [30M+48W]D

As given man twice efficient as women

M=2

W=1

36*2*16 = 36*2*4 + [30*2+48*1]D

D=8 Ans

Ex.4 If 5 men and 9 women can do A work in 19 days respectively. Then in how many days 3 men and 6 women can do this work.

Sol. 5M=9W

M/W = 9/5

M=9

W=5

9W * 19 = [3M+6W]D

9*5*19 =[3*9+6*5]D

D=15

Ex.5 If 1 man or 2 women or 3 boys can do work in 33 days then in how many days 1 man and 1 woman and 1 boy can do their work.

Sol. Man * day = D[1 + 1/2 + 1/3] = 33

D[(6+3+2)/6] = 33

D = 18 days

Method 2

1M * 33 = [1M+1W+1B]

1*6*33 = [6+3+2]D

D = 18 days Ans.

Ex.6 If 2 men and 3 women can complete a work in 10 days. while 3 men and 2 women complete the same work in 8 days then in how many days 9 men and 3 women can do this work.

Sol (2M+3W)10 = (3M+2W)8

20M + 30W = 24M+16W

M/W = 7/2

D(9M+3W) = (2M+3W)10

D(9*7+3*2) = [2*7+3*2]10

D= 200/69

Ex.7 3 men A, B, C can complete a work in such a way that A work for all the 5 days, B work for 1st and 2nd day and c work for 3,4,5 days If B and C can do as much work in 2 days as A alone does in 3 days then how many day B alone complete this work if B and C can complete the work without the help of an in 6 days.

Sol. The ratio of time B+C: A = 2:3

The ratio of work efficiency B+C: A = 3:2

B+C can do a work in 6 days then,

Total work = 6*3 = 18days

5A+2B+3C = 18

5*2 + 2B + 2C + C = 18

10+ 2(B+C) +C = 18

10+2*3 +C =18

C=2 B=1 A =2

B=18/1 = 18 Days Ans.

Ex.8 A certain number of men can do work in 60 days. If there were 8 men more it could be finished in 10 days less. How many men are there?

Sol. Let there be x men originally

x + 8 men can finish the work in 60-10 = 50days

Now,

8 men can do in 50 days what x men can do in 10 days, then

8*50 = x *10

x=40 men

Method 2

X men do the work in 60 days

and x+8 men dot the same work in 50 days

Then using the man-day formula

60*x = 50(x+8)

x = (50*8)/10 = 40 Men Ans.