Question

A and B have been employed to tile the 1 st , 2nd , 3rd floor of area x , 3x ,5x respectively. A takes 9 hours more to tile the 1 st floor than A and B together. B takes 75 hours more to tile the 2nd floor than A and B together. In how much time will A and B together be able to tile the 3 rd floor ?

Answer 1

Answer:

75 hrs

Step-by-step explanation:

A and B have been employed to tile the 1 st , 2nd , 3rd floor of area x , 3x ,5x respectively.

Let say A & B complete the 1st Floor  in      H  hrs

then A complete 1st Floor in  H + 9 hrs

A & B complete the 2nd Floor  in   3H  hrs  ( as area  is three time)

then B complete the 2nd floor in 3H + 75 hrs

then B complete the 1 st Floor in (3H + 75)/3 = H + 25 hrs

1/(H + 9) + 1/(H+25) =  1/H

=>  H(H + 25) + H(H + 9)  = (H + 9)(H + 25)

=> H² + 25H + H² + 9H = H² + 9H + 25H  + 9 * 25

=> H² = 9 * 25

=> H = 3 * 5

=> H = 15

A & B complete the 1st Floor  in 15 hrs

A & B complete the 3rd Floor  in 15*5 = 75 hrs