GATE EC 2019 Set 1 — Question 3
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General Aptitude → Quantitative Aptitude → Time & Work
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Question
It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is __________ hours.
Correct answer
(C) 4/3
Solution
This is a work-rate problem. We need to find the combined rate of work for both machines.Let the total work be 1 unit (one production order).Machine 1 completes the order in 4 hours.
So, the rate of Machine 1 () = order/hour.Machine 2 completes the order in 2 hours.
So, the rate of Machine 2 () = order/hour.When both machines work simultaneously, their rates add up.
Combined rate () =
To add these fractions, find a common denominator, which is 4.
order/hour.The time taken to complete the same order (1 unit of work) when working together is the reciprocal of the combined rate.
Time () = hours.Therefore, the time taken to complete the same order is hours.
So, the rate of Machine 1 () = order/hour.Machine 2 completes the order in 2 hours.
So, the rate of Machine 2 () = order/hour.When both machines work simultaneously, their rates add up.
Combined rate () =
To add these fractions, find a common denominator, which is 4.
order/hour.The time taken to complete the same order (1 unit of work) when working together is the reciprocal of the combined rate.
Time () = hours.Therefore, the time taken to complete the same order is hours.
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