Time And Work Ques 8
Question-
A(working alone) can complete a task in ‘$x$ ’ days. A worked alone for $6 \frac{1}{2}$ days and was then re- placed by $B$ and $C$ who (working together) completed the remaining task in 3 days. Working alone, $B$ and $C$ take ‘$0.5 x$ ’ days and 8 days respectively to complete the entire task. What is the value of $x$ ?
8
24
20
16
10
(IDBI Bank PO Exam 29.04.2018)
Show Answer
Correct Answer: 8-(3)
Solution: (3) B’s 1 day’s work $=\frac{1}{0.5 x}$ $=\frac{2}{x}$
C’s 1 day’s work $=\frac{1}{8}$
$\therefore(B+C)$ ’s 3 days’ work $=\frac{6}{x}+\frac{3}{8}$
A’s 1 day’s work $=\frac{1}{x}$
$\therefore$ A’s $\frac{13}{2}$ day’s work $=\frac{13}{2 x}$
Remaining work $=1-\frac{13}{2 x}=\frac{2 x-13}{2 x}$
$\therefore \frac{2 x-13}{2 x}=\frac{6}{x}+\frac{3}{8}$
$\Rightarrow \frac{2 x-13}{2 x}-\frac{6}{x}=\frac{3}{8}$
$\Rightarrow \frac{2 x-13-12}{2 x}=\frac{3}{8}$
$ \begin{aligned} & \Rightarrow 2 x-25=\frac{3}{8} \times 2 x=\frac{3 x}{4} \\ & \Rightarrow 8 x-100=3 x \\ & \Rightarrow 8 x-3 x=100 \Rightarrow 5 x=100 \\ & \Rightarrow x=\frac{100}{5}=20 \end{aligned} $
BETA
