Working alone A can do a job in 24 days, while B will take 12 days

Question

Working alone A can do a job in 24 days, while B will take 12 days. Working together, B and C will take 8 days; working together A and D will take 16 days. If all four of them worked together and got $ 9000 for completing the task, what is D's share of $ 9000?

A. $1000
B. $2000
C. $3000
D. $4000
E. $5000

A. $1000
B. $2000
C. $3000
D. $4000
E. $5000

CareerGeek · Answer

Assume the total work = LCM(24, 12, 8, 16) = 48

—> Rate of A, Ra = 48/24 = 2;
—> Rate of B, Rb = 48/12 = 4;

B and C will take 8 days
—> Rb + Rc = 48/8 = 6
—> Rc = 6 - 4 = 2

A and D will take 16 days
—> Ra + Rd = 48/16 = 3
—> Rd = 3 - 2 = 1

$ 9000 will be divided in the same proportion as their rates
—> Ra : Rb : Rc : Rd = 2 : 4 : 2 : 1

Share of D = 1/(2+4+2+1)*9000 = 1/9*9000 = $ 1000

Option A

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ArunSharma12 · Answer

\frac{1}{B} + \frac{1}{C} = \frac{1}{8} 
 \frac{1}{C} = \frac{1}{8}-\frac{1}{12} ; C = 24
similarly,
 \frac{1}{A} + \frac{1}{D} = \frac{1}{16} ; D = 48

ratio of the time taken by A:B:C:D=24:12:24:48 
ratio of their work done will be reverse of time taken =  \frac{1}{24}:\frac{1}{12}:\frac{1}{24}:\frac{1}{48}  = 2:4:2:1

share of D =  \frac{1*9000}{9}  =1000
Ans: A

globaldesi · Answer

find out the number of days A, B C and D can work
a= 24 days
b = 12 days
c= 24 days
d = 48
hence the ratio of the money theyget will be inverse of teh days they finish a task
hence they get money as 24: 12:24:48/48 
or 2:4:2:1
total is 9000 hence D gets 1/9 *9000 = 1000
Answer A

fireagablast · Answer

a = 1/24
b = 1/12
b+c = 1/8 -->1/12 + 1/c = 1/8 --> b=1/24
a+d = 1/16 -->1/24 + 1/d = 1/16 --> d=1/48

1= (1/24+1/12+1/24+1/48)t
1 = 9/48t
t = 48/9

dt = 1/48*48/9 = 1/9
9000*1/9 = 1000

ScottTargetTestPrep · Answer

We see that the rates of A and B are 1/24 and 1/12, respectively. If we let c and d be the number of days it takes C and D to finish the job alone by themselves, respectively, we can say that C’s rate is 1/c and D’s rate is 1/d, and we can create the equations:

1/12 + 1/c = 1/8

and

1/24 + 1/d = 1/16

Multiplying the first equation by 24, we have:

2 + 24/c = 3

24/c = 1

c = 24

Similarly, multiplying the second equation by 48, we have:

2 + 48/d = 3

48/d = 1

d = 48

So the rates of C and D are 1/24 and 1/48, respectively.

The ratio of their shares of the total sum of money is equal to the ratio of their work rates:

A : B : C : D = 1/24 : 1/12 : 1/24 : 1/48 = 2 : 4 : 2 : 1

Letting x = the amount received by D, we can create the equation:

2x + 4x + 2x + x = 9000

9x = 9000

x = 1000
 
 Answer: A

Working alone A can do a job in 24 days, while B will take 12 days

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Working alone A can do a job in 24 days, while B will take 12 days

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