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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Tango and Cash can complete certain task together in 20 days. Tango al

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Math Expert V
Joined: 02 Sep 2009
Posts: 62676
Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 73% (02:12) correct 27% (02:56) wrong based on 77 sessions

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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

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Posts: 526
Location: Poland
GMAT 1: 570 Q41 V27
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Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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2
1
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,
$$Rate * Time = Work done$$ -> $$5*Time = 160$$ -> $$Time = 32 days$$

Director  P
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Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
Posted from my mobile device

From the picture, cash alone works in 32 days
OA:E
Attachments 1580989801577421576042421540428.jpg [ 7.26 MiB | Viewed 1093 times ]

GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 6036
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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giving a try
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, 07:42.
Last edited by Archit3110 on 07 Feb 2020, 00:44, edited 2 times in total.
Director  D
Joined: 07 Mar 2019
Posts: 927
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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2
1
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.

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Manager  G
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Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
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
Manager  B
Joined: 14 Sep 2019
Posts: 220
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
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)
CR Forum Moderator D
Joined: 18 May 2019
Posts: 767
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
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.

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GMAT 1: 720 Q49 V40 GPA: 3.8
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
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.

Posted from my mobile device
Director  P
Joined: 25 Jul 2018
Posts: 614
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
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

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Senior Manager  G
Joined: 16 Feb 2015
Posts: 355
Location: United States
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
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]

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1
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

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Originally posted by GMATinsight on 06 Feb 2020, 19:36.
Last edited by GMATinsight on 06 Feb 2020, 19:44, edited 2 times in total.
Intern  Joined: 04 Feb 2020
Posts: 6
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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1
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.

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Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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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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Joined: 24 Nov 2016
Posts: 1369
Location: United States
Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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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

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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Joined: 10 Dec 2017
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Location: India
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

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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:) Re: Tango and Cash can complete certain task together in 20 days. Tango al   [#permalink] 09 Feb 2020, 03:11
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