Time and work: variation and working together

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Free questions

1. Question 1

   Consider the following statements on the multiplicative factor method. 1. The ratio of each column is written as first-row value : second-row value. 2. For a quantity in direct proportion with the unknown, the inverse of that ratio is the multiplying factor. 3. For a quantity in inverse proportion with the unknown, the inverse of the ratio is also the multiplying factor. Which of these are correct?

   1. A. 1 only
   2. B. 2 and 3 only
   3. C. 1 and 2 only
   4. D. 1, 2 and 3
   Answer and explanation

   ✓ Correct answer: C. 1 and 2 only

   Ratio = first row : second row; for direct proportion take its inverse (20 days → 12 days: factor 12/20), for inverse proportion keep it (15 women → 32 women: factor 15/32); so 1 and 2 are correct and 3 is wrong.

   Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம் (4.5 கலப்பு மாறல்), p. 148 (PDF p. 154))

2. Question 2

   Which of these pairs is in inverse variation?

   1. A. Workers and the time to finish the work
   2. B. Distance and time at a constant speed
   3. C. Things bought and the money spent
   4. D. Working hours and earnings
   Answer and explanation

   ✓ Correct answer: A. Workers and the time to finish the work

   Two quantities are in inverse variation when their product is constant (xy = k): for the same work, workers × time stays the same, so more workers need less time; distance and time at a constant speed, purchase and spending, and working hours and earnings vary directly (y/x = k).

   Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம் (4.5 கலப்பு மாறல்), p. 147 (PDF p. 153))