WORK - Interesting problem

[kvamsy]

Three men or five women can construct the wall in 68 days. how long will it take for 5men and 3 women to complete the same job.

A) 25
B) 35
C) 30
D) 40
E) 42.5

[outreach]

m- work done by a man in a day
w- work done by a woman in a day

3m=(1/68)
m=(1/68*3)
5m=(5/68*3)


5w=(1/68)
w=(1/68*5)
3w=(3/68*5)

5m+3w=(5/68*3)+(3/68*5)
=(1/30)

answer is C

[thephoenix]

3m=5w--->1m=5/3w--->5m=25w/3

5m+3w=25w/3+3w=34w/3

now eqn is 5w*68=34/3w*x(days)
--->x=30 days

[alwayslulu]

wow! I look both explanation and still don't understand how can u get 30 days? my head is spinning now. ~

more clarification would be very much appreciated!

~Lulu

[eaakbari]

Rate of work = 1/ time taken

or another way to look at it is if person takes t days to do one job
each day he is doing 1/t amount of work

So since 3 men took 68 days
3/x = 1/68

So 1/x = 1/(3*68)

In the same fashion 1/y = 1/(5*68)

Now since 5 men and 3 women are working

5/(3*68) + 3/(5*68)

On solving we get
1/30

hence each day they do 1/30 work

So they take 30 days in all
Hope this explains

[thephoenix]

wow! I look both explanation and still don't understand how can u get 30 days? my head is spinning now. ~

more clarification would be very much appreciated!

~Lulu

actually i made veru short....appologies

formula to remeber in such problems
M1*D1=M2*D2=work done
in such problems always try to convert in one catogery either boy or men or women( there will be always some hint in q)
in this one
Three men or five women can construct the wall in 68 days------>(gives us) 3m=5w( becoz there eff are same)
or 3m*68=5w*68--->3m=5w[using formula m1*d1=m2*d2]
from abve 1m=5w/3
so 5m+3w---->5(5w/3)+3w=34w/3
now again using the same formula
5w*68=34w/3*(say)x days---->solvingx=30 days
hth

[alwayslulu]

thanks for the explanation.

M1*D1=M2*D2=work done . Is M men? and D days? what is the general formula? is it W = R.T or R= W.T ? i'm so confused


And when can i use this formula (A*B)/(A+B) ?