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 ?
A. 3 days
B. 9 days
C. 12 days
D. Cannot be determined
E. None of these
Answer: Option E
Solution(By Examveda Team)
$$\eqalign{ & {\text{A's 1 day's work}} \cr & = \frac{1}{{{\text{T}} + 3}} \cr & {\text{B's 1 day's work}} \cr & = \frac{1}{{{\text{T}} + 12}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{{\text{T}}} \cr & \therefore \frac{1}{{{\text{T}} + 3}} + \frac{1}{{{\text{T}} + 12}} = \frac{1}{{\text{T}}} \cr & \Rightarrow \frac{{2{\text{T}} + 15}}{{\left( {{\text{T}} + 3} \right)\left( {{\text{T}} + 12} \right)}} = \frac{1}{{\text{T}}} \cr & \Rightarrow 2{{\text{T}}^2} + 15{\text{T}} = {{\text{T}}^2} + 15{\text{T}} + 36 \cr & \Rightarrow {{\text{T}}^2} = 36 \cr & \Rightarrow {\text{T}} = 6 \cr} $$Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
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