Mary and Jane working together can complete a task in 2 hours and 24 m

m+j = 5/12---------------1( work done by m and j in 1 hr )
j + k= 3/4------------------2 ( work done in 1 hr )
k+m = 2/3----------------3( work done in 1 hr)

add eq 1,2 3
2 ( j+ K+ m) = 5/12 + 3/4 + 2/3
j+k+M = 22/12 * 1/2 = 11/12 ( the total work done by j, k, m in 1 hr)

Now we are left with 1/12 of work
1- (11/12) = 1/12
Approx 1/12 work is done in 6 mins
So 60 min + 6 = 66 min

E is correct

M + J = 144 Min
J + K = 80 Min
K + M = 90 Min

Let, the total work be 720 Units...

Efficiency of M + J = 5
Efficiency of J + K = 9
Efficiency of K + M = 8

Total efficiency of K + M + J = (5+9+8)/2 = 11

So, Total time taken by K + M + J is 720/11 ~ 65.xxx, Answer must hence be (E)

IMO-D


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m+j= 144
j+k=80
k+m=90

adding gives:

2m + 2j + 2k = 314
m+j+k= 157

Can you explain where i am going wrong?

harshsaini could you please explain how did you get 1/12 work will be done in 6 minutes?

M+J can complete the task in 2 hrs 24 mins or (12/5)hrs (i.e. they can do (5/12)th of the task in 1 hr)
J+K .................................. 1 hr 20 mins or (4/3) hrs. (i.e. they can do (3/4)th of the task in 1hr)
K+M.................................. 1 hr 30 mins or (3/2) hrs. (i.e. they can do (2/3)rd of the task in 1 hr)

Let us assume that, working alone, M, J and K can complete the task in 'm', 'j' and 'k' hrs respectively. Then:

In 1 hr, (M+J) can do [(1/m)+(1/j)]th of the task. So:

(1/m)+(1/j)=(5/12)....... (I)
Similarly:
(1/j)+(1/k)=(3/4).......... (II)
(1/k)+(1/m)=(2/3)........ (III)

Subtracting (I) from (II), we get:
(1/j)+(1/k)-(1/m)-(1/j)=(3/4)-(5/12)....> (1/k)-(1/m)=(1/3)....> (1/k)=(1/m)+(1/3) which means that, in 1 hr, K can do whatever fraction of the task M can do plus (1/3)rd more.
From (III), we have:
(1/k)+(1/m)=2/3...[(1/m)+(1/3)]+(1/m)=(2/3)....> m=6.....>(1/k)=(1/6)+(1/3).....>k=2. Substituting this in (II), we get: j=4

So, working together, M, J and K can, in 1 hr, do [(1/m)+(1/j)+(1/k)]th of the task or:

(1/6)+(1/4)+(1/2)=(11/12)th of the task.
All three working together can complete the task in (12/11) hrs or 65.45 minutes.
ANS: E