GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Apr 2020, 21:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62456
Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 01:18
00:00

Difficulty:

45% (medium)

Question Stats:

73% (02:10) correct 27% (02:57) wrong based on 75 sessions

### HideShow timer Statistics

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

_________________
Senior Manager
Joined: 14 Dec 2019
Posts: 494
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 01:50
1
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,
$$Rate * Time = Work done$$ -> $$5*Time = 160$$ -> $$Time = 32 days$$

Senior Manager
Joined: 01 Mar 2019
Posts: 484
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 03:51
1
Posted from my mobile device

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

1580989801577421576042421540428.jpg [ 7.26 MiB | Viewed 1067 times ]

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6049
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]

### Show Tags

Updated on: 07 Feb 2020, 00:44
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
Joined: 07 Mar 2019
Posts: 910
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]

### Show Tags

06 Feb 2020, 09:34
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.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager
Joined: 30 Jul 2019
Posts: 101
Location: Viet Nam
Concentration: Technology, Entrepreneurship
GPA: 2.79
WE: Education (Non-Profit and Government)
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 10:18
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
Joined: 14 Sep 2019
Posts: 220
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 10:49
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
Joined: 18 May 2019
Posts: 800
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 13:51
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.

Director
Joined: 30 Sep 2017
Posts: 801
GMAT 1: 720 Q49 V40
GPA: 3.8
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 15:02
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
Joined: 25 Jul 2018
Posts: 642
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

06 Feb 2020, 15:11
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

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

### Show Tags

06 Feb 2020, 18:49
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
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3434
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

Updated on: 06 Feb 2020, 19:44
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

_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi

My Recent Posts Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Standard Deviation l Q-4-Functions
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION

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]

### Show Tags

06 Feb 2020, 19:36
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.

CEO
Joined: 03 Jun 2019
Posts: 2506
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

07 Feb 2020, 01:58
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
VP
Joined: 24 Nov 2016
Posts: 1359
Location: United States
Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

07 Feb 2020, 06:41
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)
Manager
Joined: 10 Dec 2017
Posts: 177
Location: India
Re: Tango and Cash can complete certain task together in 20 days. Tango al  [#permalink]

### Show Tags

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