Arun makes a popular brand of ice-cream in a rectangular shaped bar 6 cm long,…
2024
Arun makes a popular brand of ice-cream in a rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain the same, but the length and width will be decreased by the same percentage. The new width will be?
- A.
4.5cm
- B.
5.5cm
- C.
6.5 cm
- D.
7.5cm
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Correct answer: A
Solution: Find the new width after a 19% reduction in volume when thickness stays the same and length and width are reduced by the same percentage.
Compute the original volume: 6 × 5 × 2 = 60 cm³.
After a 19% reduction the new volume is 60 × (1 − 0.19) = 60 × 0.81 = 48.6 cm³.
Thickness stays 2 cm, so the product length × width must be 48.6 ÷ 2 = 24.3. This is 0.81 times the original length × width (which was 6 × 5 = 30).
If both length and width are reduced by the same factor s, then s² = 0.81, so s = √0.81 = 0.9 (take the positive root since s is a scale factor).
New width = 5 × 0.9 = 4.5 cm.
Answer: 4.5 cm.
Quick check: New length = 6 × 0.9 = 5.4 cm, so new volume = 5.4 × 4.5 × 2 = 48.6 cm³, which is 19% less than 60 cm³.