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Machines A and B produce 8000 clips in 4 hours and 5 hours respectively. If they work alternately for 1 hour, B starting first, then in how many hours 8000 clips will be produced?

Machines A and B produce 8000 clips in 4 hours and 5 hours respectively. If they work alternately for 1 hour, B starting first, then in how many hours 8000 clips will be produced? Correct Answer 4.5 hours

Given:

Machines A and B produce 8000 clips in 4 hours and 5 hours respectively.

Concept Used:

Concept of unitary method

Unitary Method: The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Calculation:

In 1 hour machine A can produce 8000/4 = 2000 clips

In 1 Hour machine B can produce 8000/5 = 1600 clips

Starting with B in 2 hours B and A can produce (2000 + 1600) = 3600 

⇒ In 4 hours B and A can produce 3600 × 2 = 7200 clips

Now machine B will start producing

Remaining to complete the target = (8000 - 7200) = 800

To produce to 800 clips machine B will take time = 800/1600 = 0.5 hours

Total time to complete the production = (4 + 0.5) = 4.5 hours

∴ In 4.5 hours 8000 clips will be produce.

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