Question

two workers A and B start some work if A was alone then take 8 hours more than a and b works together and if B was alone then take 9 /2 hours more than a and b works together then find out in how much time they finished if they work together

Answer 1

Let A & B take 'x' hours to complete a work
Then, A takes (x+8) hours and B takes (x + 9/2) hours to complete the same work.

In 1 hour:
A & B do 1/x part of the work
A does 1/x+8 part of the work
B does 1/(x+9/2) part of the work

So:
1/x = 1/x+8 + 1/(x+9/2)
1/x = 1/x+8 + 2/2x+9
1/x = (2x+9+2x+16)/(x+8)(2x+9)
1/x = 4x+25/2x^2+9x+16x+72 = (4x+25)/(2x^2+25x+72)
x = (2x^2+25x+72)/(4x+25)
4x^2 + 25x = 2x^2 + 25x + 72
2x^2 = 72
x^2 = 36
x = 6...A&B=6hrs, A alone=14hrs, B alone=10.5hrs

Hence A & B together can finish the work in 6 hours
Hope this helps