A and B together complete a piece of work in T days. If A alone compl…

Question

A and B together complete a piece of work in T days. If A alone completes the work in T + 3 days and B alone completes the piece of work in T + 12 days, what is T ?

Accepted Answer

Option E. None of these. Answer & Solution Answer: Option E Solution: & A's 1 day's work & = 1 T + 3 & B's 1 day's work & = 1 T + 12 & ( A + B ) 's 1 day's work = 1 T & 1 T + 3 + 1 T + 12 = 1 T & 2 T + 15 ( T + 3 ) ( T + 12 ) = 1 T & 2 T^2 + 15 T = T^2 + 15 T + 36 & T^2 = 36 & T = 6