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20 Oct 2013, 13:42
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (03:05) correct
71%
(03:23)
wrong
based on 184
sessions
History
Date
Time
Result
Not Attempted Yet
Three men A, B and C working together can do a work in 30 days. They start the work together and A works for 3 days and takes rest on the fourth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)
A. 39
B. 40
C. 42
D. 41
E. 45
A. 39
B. 40
C. 42
D. 41
E. 45
20 Oct 2013, 14:20
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abhishekkhosla
Total work is 3*30 = 90 units.
A's schedule WWWR 3 workdays in 4.
B's schedule WWWWWRR 5 workdays in 7.
C's schedule WWWWWWWRRR 7 workdays in 10.
Test the options. In 40 days:
A will do 10*3=30 units (10 complete cycles).
B will do 5*5+5=30 units (5 complete cycles and 5 days of work).
C will do 4*7=28 units (4 complete cycles).
Total = 88 units.
On 41st day, A and C will work and do 2 units of work, so in 41 days 88+2=90 units of work will be done.
Answer: D.
P.S. Not a GMAT question.
05 Nov 2013, 12:09
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Bunuel
I took a slightly different approach and got C as the answer. Here it goes:
A's schedule lasts 4 days, B's schedule lasts 7 days, C's schedule lasts 10 days. Now, LCM of 4,10 and 7 is 140 days.
For A: In 4 days, A works for 3 days. Therefore in 140 days, A will work for \(105 days\).
For B: In 7 days, B works for 5 days. Therefore in 140 days, B will work for \(100 days\).
For C: In 10 days, C works for 7 days. Therefore in 140 days, C will work for \(98 days\).
Now, the total days worked = \((105 + 100 + 98)= 303 workdays\)
To achieve 303 workdays we need 140 days. Therefore to achieve 90 workdays we need \(\frac{90*140}{303}\)= 41.6(approx) = 42 days.
