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Tango and Cash can complete certain task together in 20 days. Tango al

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Bunuel
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Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   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


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E
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   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.
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   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
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 16:11
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Ind. efficiency (Tango) —\(\frac{1}{32 }\)
Ind. efficiency (Cash) —\(\frac{1}{x}\)
—> when they work together, their individual efficiency drop by 20%

\(0.8*( \frac{1}{32}+ \frac{1}{x}) = \frac{1}{20}\)

\(\frac{1}{32} + \frac{1}{x} = \frac{1}{16}\)

(32 + x)*16 = 32x
32*16 + 16x = 32x
—> x = 32 days

The answer is E

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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   Updated on: 06 Feb 2020, 20:44
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Quote:
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


Method 1:

CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)
i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

\(\frac{0.8*(T+C)*20}{1} = \frac{T*32}{1}\)
i.e. 16T + 16 C = 32T
i.e. C = T
i.e. Cash also takes 32 days

Method-2

With 20% less efficiency Tango and Cash take = 20 days
i.e. With 80% efficiency, Tango and Cash take = 20 days

CONCEPT: Efficiency is Inversely proportion to the Time

i.e. With 100% efficiency, Tango and Cash take = 20*0.8 = 16 days

Tango alone takes 32 days

i.e Cash's one day work = (1/16)-(1/32) = 1/32

i.e. Cash takes 32 days

Answer: Option E

Originally posted by GMATinsight on 06 Feb 2020, 20:36.
Last edited by GMATinsight on 06 Feb 2020, 20:44, edited 2 times in total.
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 04:51
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Posted from my mobile device

From the picture, cash alone works in 32 days
OA:E
Attachments

1580989801577421576042421540428.jpg
1580989801577421576042421540428.jpg [ 7.26 MiB | Viewed 5370 times ]

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Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   Updated on: 07 Feb 2020, 01:44
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by decrease in efficiency it means no of days of work will increase so T will take now 32/.8 ;
40 days
1/40 +1/c = 1/20
c= 40 @ 80% efficiency
so 100 % ; 40 * .8 ; 32
IMO E

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

Originally posted by Archit3110 on 06 Feb 2020, 08:42.
Last edited by Archit3110 on 07 Feb 2020, 01:44, edited 2 times in total.
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 11:18
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Quote:
Tango and Cash can complete a 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?


In one day, Tango alone can do \(\frac{1}{32}\) the task, and Cash alone can do x the same task.

When both work together their individual efficiencies drop by 20% compared to the efficiencies they have when they work alone
=> \(( \frac{1}{32} + x ) * ( 1 - \frac{1}{5} ) * 20 = 1\)
=> x = \(\frac{1}{32}\)
=> Cash alone can complete the same task in 32 days.
=> Choice E
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 11:49
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Number of days = 1/Efficiency.
When they work alone, they can complete the work in 20(4/5) days = 16 days.
Suppose, Cash can complete the task alone in x days.
1/x + 1/32 = 1/16
1/x = 1/16 – 1/32
1/x = (2-1)/32 = 1/32

Hence, Cash can complete the task in 32 days.(E)
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 14:51
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We are informed that when Tango and Cash work together they are able to complete a piece of work in 20 days. Tango working alone can complete the work in 32 days. The caveat, however, is that when they work together, their individual efficiencies drop by 20%, implying individually, Tango and Cash working together will work individually at 80% of the rate at which each person works individually.

So Tango's revised rate = 32/0.8 = 32*10/8 = 40 days
Cash's revised rate, C, when working with Tango => 1/C + 1/40 = 1/20
Hence 1/C = (2-1)/40 = 1/40
Hence Cash's rate when working alone = 0.8*40 = 32 days.

The answer is E.
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 16:02
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80% * (1/32 + 1/C) = 1/20
(1/32 + 1/C) = 1/16
1/C= 1/32 --> C = 32 days

So, Cash alone can complete the same task in 32 days.

FINAL ANSWER IS (E)

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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 20:36
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Let us assume the total work to be done is 100 units.

C and T together can complete the work in 20 days ==> the Rate @ which C and T together working at Same time is 100 / 20 = 5 units per day

But 5 = 80 % efficency of C + 80% effiicency of T

Now T alone can complete 100 units of work in 32 days ==> the Rate @ which T does work is 100 / 32

and 80% efficiency of T = (100 /32 ) * (4/5) = 5/2 = 2.5

We know that 80 % efficiency of C + 80% efficiency of T = 5 ==> 80 % efficiency of C = 5 - 80 % efficiency of T = 5 - 2.5 = 2.5

therefore 80% efficiency of C = 2.5 or 5 / 2 . and 100 % efficiency of C = (5/2) *(5/4) = 25/8

so the rate at which C does work is 25/8 units per day and 100 units can be completed in 32 days.

Answer: 32 (E)
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   06 Feb 2020, 19:49
Explanation:
T can do work in 32days.
Working both, efficiency decrease by 20%
So, Eqn :
0.8 (1/T + 1/C) = 1/20
0.8x(1/32) + 0.8/C = 1/20
C=32

Cash can complete work in 32 days.

IMO-E
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   07 Feb 2020, 02:58
Bunuel wrote:

Competition Mode Question



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


Given:
1. Tango and Cash can complete certain task together in 20 days.
2. Tango alone can do the same task in 32 days.
3. When both work together their individual efficiencies drop by 20% compared to the efficiencies they have when they work alone.

Asked: In how many days Cash alone can complete the same task?

Let us assume that Cash alone can complete the same task in x days.

(1/x + 1/32).8 = 1/20
1/x + 1/32 = 1/(20*.8) = 1/16
1/x = 1/16 - 1/32 = 1/32
x = 32

IMO E
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Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   07 Feb 2020, 07:41
Quote:
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


rate*time=work
t=1/32
4/5(t+c)=1/20
t+c=1/20*5/4=5/80=1/16
c=1/16-32=2-1/32=1/32

Ans (E)
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   09 Feb 2020, 04:11
Bunuel wrote:

Competition Mode Question



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

0.8(T+C)=1/20
T+C=1/16
T=1/32
C=1/32
E:)
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink] New post   20 Apr 2022, 18:10
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Re: Tango and Cash can complete certain task together in 20 days. Tango al [#permalink]
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