Question

How long will Machine $Y$, working alone, take to produce $x$ candles?
$I$. Machine $X$ produce $x$ candles in $5$ minutes.
$II$. Machine $X$ and Machine $Y$ working at the same time produce $x$ candles in $2$ minutes.

• A. $I$ alone sufficient while $II$ alone not sufficient to answer
• B. $II$ alone sufficient while $I$ alone not sufficient to answer
• C. Either $I$ or $II$ alone sufficient to answer
• D. Both $I$ and $II$ are not sufficient to answer
• E. Both $I$ and $II$ are necessary to answer

Answer 1

The correct option is E Both $I$ and $II$ are necessary to answer

$I$. gives, Machine $X$ produces $\frac{x}{5}$ candles in $1$ min.
$II$. gives, Machine $X$ and $Y$ produce $\frac{x}{2}$ candles in $1$ min.
From $I$ and $II$, $Y$ produces $(\frac{x}{2}-\frac{x}{5})=\frac{3x}{10}$ candles in $1$ min.
$\frac{3x}{10}$ candles are produced by $Y$ in $1$ min.
$x$ candles will be produced by $Y$ in $\left(\frac{10}{3x}xx\right)min=\frac{10}{3}$ min.
Thus, $I$ and $II$ both are necessary to get the answer.
$\therefore$ Correct answer is (E).