Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
A child can do a piece of work 15 hours slower than a woman. The child works for 18 hours on the job and then the woman takes charge for 6 hours. In this manner, $\frac{3}{5}$ of the work can be completed. To complete the job now, how much time will the woman take? (M.A.T., 2005)
(a)12 hours
(b)18 hours
(c)24 hours
(d)30 hours
Answer
Answer (as printed): A
Explanation
Suppose the woman takes $x$ hours to do the job. Then, the child takes $(x+15)$ hours to do the job. Woman's 1 hour's work $=\frac{1}{x}$. Child's 1 hour's work $=\frac{1}{(x+15)}$. Child's 18 hours' work + Woman's 6 hours' work $=\frac{3}{5}$ $\Rightarrow \frac{18}{(x+15)}+\frac{6}{x}=\frac{3}{5} \Rightarrow \frac{18x+6(x+15)}{x(x+15)}=\frac{3}{5}$ $\Rightarrow 5(24x+90)=3(x^{2}+15x)$ $\Rightarrow 120x+450=3x^{2}+45x$ $\Rightarrow 3x^{2}-75x-450=0$ $\Rightarrow x^{2}-25x-150=0$ $\Rightarrow x^{2}-30x+5x-150=0$ $\Rightarrow x(x-30)+5(x-30)=0$ $\Rightarrow (x-30)(x+5)=0 \Rightarrow x=30$. Remaining work $=\left(1-\frac{3}{5}\right)=\frac{2}{5}$. $\frac{1}{30}$ work is done by the woman in 1 hour. $\therefore \frac{2}{5}$ work will be done by the woman in $\left(30 \times \frac{2}{5}\right)=12$ hours.
Explanation as extracted from the printed page; notation may be imperfect.