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

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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

A. 24
B. 26
C. 28
D. 30
E. 32

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unraveled · Accepted Answer

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

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.

shameekv1989 · Answer

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

madgmat2019 · Answer

Posted from my mobile device

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

Archit3110 · Answer

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

A. 24
B. 26
C. 28
D. 30
E. 32

ostrick5465 · Answer

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

Jawad001 · Answer

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)

eakabuah · Answer

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.

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.

freedom128 · Answer

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)

Posted from my mobile device

lacktutor · Answer

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
 
   Posted from my mobile device

rajatchopra1994 · Answer

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

GMATinsight · Answer

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

KalyanChamarthi · Answer

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)

Kinshook · Answer

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

exc4libur · Answer

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)

satya2029 · Answer

0.8(T+C)=1/20
T+C=1/16
T=1/32
C=1/32
E:)

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