Question : $x$ can copy 80 pages in 20 hours $x$ and $y$ together can copy 135 pages in 27 hours. Then $y$ can copy 20 pages in:
Option 1: 20 hours
Option 2: 3 hours
Option 3: 24 hours
Option 4: 12 hours
Correct Answer: 20 hours
Solution :
Assuming that $x$ efficiency is $e_x$ and $y$ efficiency is $e_y$.
Given that $x$ can copy 80 pages in 20 hours,
$⇒e_x = \frac{\text{pages}}{\text{time}} = \frac{80}{20} = 4$
Given that $x$ and $y$ together can copy 135 pages in 27 hours,
$⇒e_x + e_y = \frac{\text{pages}}{\text{time}} = \frac{135}{27} = 5$
Substituting the value of $e_x$ in the above equation,
$⇒4 + e_y = 5$
Solving for $e_y$, we get:
$⇒e_y = 1$
If, $y$ can copy 1 page in 1 hour.
Therefore, $y$ can copy 20 pages in 20 hours.
Hence, the correct answer is 20 hours.
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