Neco 2024 Mathematics Question 10

Practice essay / theory question 10 from the 2024 Neco Mathematics examination. This question covers Variation .

Neco 2024 Mathematics Essay / Theory
Topic: Variation
Question 10 NECO • 2024 • MATHEMATICS • essay

In a manufacturing process the time \(T\) (in minutes) taken to complete a fixed batch varies directly as the square of the number of workers \(w\) and inversely as the efficiency rating \(E\) of the machine. When 5 workers operate a machine with efficiency rating 8, the batch is completed in 20 minutes.

Question Parts

( a )
Determine the constant of variation \(k\) and write the formula that relates \(T\), \(w\) and \(E\).
( b )
If the efficiency rating is increased to 12, how many workers are required to reduce the time to 15 minutes? Give your answer to one decimal place.
( c )
Keeping the number of workers at 6, by what factor must the efficiency be increased so that the time taken is halved compared with the original 20‑minute time? Express the required efficiency as a multiple of the original efficiency.

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About This Question

This is Neco 2024 Mathematics Question 10. It is one of the essay questions from the 2024 Neco Mathematics examination.

The question covers Variation .

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