Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
A takes 5 days more than B to do a certain job and 9 days more than C; A and B together can do the job in the same time as C. How many days A would take to do it?
(a)5
(b)10
(c)15
(d)20
Answer
Answer (as printed): C
Explanation
Suppose A takes $x$ days to do the job alone. Then, B takes $(x-5)$ days and C takes $(x-9)$ days. (A+B)'s 1 day's work = C's 1 day's work $\Rightarrow \frac{1}{x}+\frac{1}{(x-5)}=\frac{1}{(x-9)} \Rightarrow \frac{(x-5)+x}{x(x-5)}=\frac{1}{(x-9)} \Rightarrow (2x-5)(x-9)=x(x-5) \Rightarrow 2x^{2}-23x+45=x^{2}-5x \Rightarrow x^{2}-18x+45=0 \Rightarrow (x-3)(x-15)=0 \Rightarrow x=15$. [$\because x \neq 3$] Hence, A alone would take 15 days to do the job.
Explanation as extracted from the printed page; notation may be imperfect.