Q5--------ïƒ A takes 5 days more than .......................?

Question

Q5--------A takes 5 days more than B to do a certain job and 9 days more than C;A and B together can do the job in the same time as C.How many days A would take to do it.

a. 16 days

b. 10 days

c. 15 days

d. 20 daya

Answer 1

Answer is  c i.e. 15 days.

I hope this is not your home work question :)

Answer in detail

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Assume  

  A takes x days to finish a given job.

So,

  B will take x -5 days to finish the same job

  c will take  x- 9 days to finish the job

  Now, in one day

  A  will finish   1/x of the job

  B  will finish   1/(x-5) of the job

  C Will finish   1/(x-9) of the job.

[A and B together can do the job in the same time as C]

Hence in one day, combined effort of A and B is equal to C's  effort

i.e.   (  1/x + 1/(x-5) )   = 1/(x-9)

=>     ( x -5 +x)/(x^2  -5x) = 1/(x-9)

=>     (2x-5)/(x^2 -5x)  = 1/(x-9)

After cross multiplication

=>    (2x-5)*(x-9) = x^2 -5x

=>   2x^2 -5x -18x + 45 = x^2 -5x

After further implication  

=> x^2 -18x +45 = 0

Make some adjustment to have it in (x-y)^2 = z^2  form

=> x^2 - 2*9x  +81 -81+45 = 0

=>  x^2 - 2*9x  +81 -36 = 0

=>  (x -9)^2 = 36

=>  (x -9)^2 = 6^2

Simplify the equation

=> x-9 = 6

Therefor x = 15

So, x takes 15 days to finish the job.