Question

A take 10days less thantime taken by b to finisha peice of work. if a and b together can finish the work in 12 days find the time takenby b to finish the work

Answer 1

A takes 10 days less than time taken by B to finish piece of work so,
A = B - 10.......(1)

let take x as time taken to finish a piece of work by
B = x
then A = x-10

one day work of A,
A= 1/(x-10)
one day work of B,
B = 1/x

A and B work together to finish a job in 12 days so,
A+B = 12

one day work of A and B
A+B = 1/12..........(2)

substitute A and B in (2)
1/(x-10) + 1/x = 1/12
(x+x-10)/(x*(x-10)) = 1/12
(2x - 10)*12 = x²-10x
24x - 120 = x²-10x
x²-10x-24x+120 = 0
x²-34x+120 = 0
x²-4x-30x+120 = 0
x(x-4)-30(x-4) = 0
(x-4)(x-30) = 0
x= 4,30

B finish a job in x= 4 days is not possible because A and B work together for 12 days so B time taken to finish a should be greater than 12

so B finish the job in x=30 days

A finish the same job in x-10 = 30-10 = 20 days

to check whether A=20, B=30

one days work of A and B together,

A+B = 1/20+1/30
A+B = (30+20)/600
A+B = 50/600
A+B = 1/12

time taken to finish whole work of A and B together

A+B = 12