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

Question

GMATbuster's Weekly Quant Quiz#11 Ques #10 
 For Questions from earlier quizzes:  Click Here

Mary and Jane working together can complete a task in 2 hours and 24 minutes. Jane and Karen working together can complete the same task in 1 hour 20 minutes whereas Karen and Mary working together can complete the task in 1 hour 30 minutes. Which of the following best represents the time (in minutes) taken to complete the task if Mary, Jane and Karen work together?

A)42
B)48
C)54
D)60
E)66

A)42 
B)48
C)54
D)60
E)66

RajatVerma1392 · Accepted Answer

Hi,
 
As R * T = W
As per the question, time taking in minutes :
M + J = 144
J + K = 80
K + M = 90

These are the timings, so we should take consider a Work total that is divisible by all of three: LCM for (144,80,90) that is = 720

Then, Total Work = 720

Rate per person:
M + J =  \frac{720}{144}  = 5
J + K = 9
K + M = 8

Thus we got individually two person rate also.
Now if they work together, then the time took:
2(M + J + K) = (5+9+8) = 22
=> M + J + K = 11 (This is the rate)

So, time took:
Total Work / Total Rate
= 720/11
= 65.45
=> 66 Minutes

Thus the answer is E.

Please hit kudos if you like the solution.

ankitahyd2013 · Answer

IMO-D

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harshsaini · Answer

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

Mansoor50 · Answer

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?

shrik · Answer

In this type of approach consider work done to be the LCM of three values

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

consider total work done to be 144

SO,

rate of M+J = 1 SINCE rate = work/time

rate of J+K = 1.8

rate of K+M =1.6

total rate equation will be

(M+J)+(J+K)+(K+M) = 1+1.8+1.6

2 ( M+J+K) = 4.4

(M+J+K) = 2.2

TOTAL WORK DONE = TOTAL RATE * TOTAL TIME

144 /2.2 = 65.45 approx 66 min

please let me know if i went wrong , if not, do consider kudos!

DarkHorse2019 · Answer

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

effatara · Answer

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  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)=(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  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

Abhishek009 · Answer

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)

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

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