TWO WORKERS A AND B ARE ENGAGED TO DO A WORK. A WORKING ALONE TAKES 8 HOURS MORE TO COMPLETE THE JOB THAN IF BOTH WORKED TOGETHER. IF B WORKED ALONE, HE WOULD NEED 4 1/2 HOURS MORE TO COMPLETE THE JOB THAN THEY BOTH WORKING TOGETHER. WHAT TIME WOULD THEY TAKE TO DO THE WORK TOGETHER? Options.
A) 4 hours B) 5 hours C) 6 hours D) 7 hours E) none of these

Rationale: let a and be together take x hours to complete the work . then , a alone takes ( x + 8 ) hrs and b alone takes ( x + 9 / 2 ) hrs to complete the work . then , 1 / ( x + 8 ) + 1 / ( x + 9 / 2 ) = 1 / x , 1 / ( x + 8 ) + 2 / ( 2 x + 9 ) = 1 / x x ( 4 x + 25 ) = ( x + 8 ) ( 2 x + 9 ) 2 x ^ 2 = 72 , x ^ 2 = 36 , x = 6 correct option : c
Answer: C