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06 Feb 2020, 02:18
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Tango and Cash can complete certain task together in 20 days. Tango alone can do the same task in 32 days. When both work together their individual efficiencies drop by 20% compared to the efficiencies they have when they work alone. In how many days Cash alone can complete the same task?
A. 24
B. 26
C. 28
D. 30
E. 32
Are You Up For the Challenge: 700 Level Questions
06 Feb 2020, 10:34
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Tango and Cash can complete certain task together in 20 days. Tango alone can do the same task in 32 days. When both work together their individual efficiencies drop by 20% compared to the efficiencies they have when they work alone. In how many days Cash alone can complete the same task?
A. 24
B. 26
C. 28
D. 30
E. 32
If Tango's 100% efficient then he takes 32 days to complete a task.
While if he is 80% efficient then he takes \(\frac{32}{0.8}\) days i.e. 40 days
Now,
\(\frac{1}{T} + \frac{1}{C} = \frac{1}{20}\) where T and C are number of days taken by Tango and Cash respectively to complete the task while 80% efficient.
\(\frac{1}{40} + \frac{1}{C} = \frac{1}{20}\)
\(\frac{1}{C} = \frac{1}{20} - \frac{1}{40}\)
\(\frac{1}{C} = \frac{1}{40 }\)
C = 40 @80% efficiency.
C = 32 @100% efficiency.
IMO Answer E.
A. 24
B. 26
C. 28
D. 30
E. 32
If Tango's 100% efficient then he takes 32 days to complete a task.
While if he is 80% efficient then he takes \(\frac{32}{0.8}\) days i.e. 40 days
Now,
\(\frac{1}{T} + \frac{1}{C} = \frac{1}{20}\) where T and C are number of days taken by Tango and Cash respectively to complete the task while 80% efficient.
\(\frac{1}{40} + \frac{1}{C} = \frac{1}{20}\)
\(\frac{1}{C} = \frac{1}{20} - \frac{1}{40}\)
\(\frac{1}{C} = \frac{1}{40 }\)
C = 40 @80% efficiency.
C = 32 @100% efficiency.
IMO Answer E.
General Discussion
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 827
06 Feb 2020, 02:50
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Rate of Tango = a
Rate of Cash = b
Rate when working together = \(\frac{4*(a+b)}{5}\)
Time for Tango = 32 days
Time for Cash = ?
Time when working together = 20 days
Assume work units = 160 (LCM of 32 and 20) for easier calculations
For Tango,
\(Rate * Time = Work done\) -> \(32*a = 160\) -> \(a=5\)
When Working together,
\(Rate * Time = Work done\) -> \(\frac{4*(a+b)}{5}\)*20 = 160 -> Solving we get \(b=5\)
Therefore For Cash,
\(Rate * Time = Work done\) -> \(5*Time = 160\) -> \(Time = 32 days\)
Answer - E
Rate of Cash = b
Rate when working together = \(\frac{4*(a+b)}{5}\)
Time for Tango = 32 days
Time for Cash = ?
Time when working together = 20 days
Assume work units = 160 (LCM of 32 and 20) for easier calculations
For Tango,
\(Rate * Time = Work done\) -> \(32*a = 160\) -> \(a=5\)
When Working together,
\(Rate * Time = Work done\) -> \(\frac{4*(a+b)}{5}\)*20 = 160 -> Solving we get \(b=5\)
Therefore For Cash,
\(Rate * Time = Work done\) -> \(5*Time = 160\) -> \(Time = 32 days\)
Answer - E
