Question : If $x$ can finish a job in 4 hours and $y$ can finish the same job in 8 hours independently, then they together will finish the job in:
Option 1: 140 minutes
Option 2: 160 minutes
Option 3: 120 minutes
Option 4: 150 minutes
Correct Answer: 160 minutes
Solution :
Assume that $x$ efficiency is $e_x$ and $y$ efficiency is $e_y$.
Let's assume that the work is 1 unit.
Given that $x$ can finish a job in 4 hours.
$⇒e_x = \frac{\text{work}}{\text{time}} = \frac{1}{4}$
Given that $y$ can finish the same job in 8 hours.
$⇒e_y = \frac{\text{work}}{\text{time}} = \frac{1}{8}$
When they work together, their combined efficiency is the sum of their efficiencies.
$⇒e_{x+y} = e_x + e_y = \frac{1}{4} + \frac{1}{8} = \frac{3}{8}$
Therefore, they will finish the job together in $\frac{8}{3}$ hours or $\frac{8}{3}$×60 minutes i.e., 160 minutes.
Hence, the correct answer is 160 minutes.
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