If the length of a room is decreased by 10% and breadth is decreased by 20%,…
2019
If the length of a room is decreased by 10% and breadth is decreased by 20%, while height is increased by 5%, then what percentage changed in the volume of the room?
- A.
24%
- B.
24.4%
- C.
24.2%
- D.
24.6%
Attempted by 1 students.
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Correct answer: B
Let the original length, breadth, and height of the room be L, B, and H respectively.
Original volume = L × B × H.
After changes:
New length = L - 10% of L = 0.9L
New breadth = B - 20% of B = 0.8B
New height = H + 5% of H = 1.05H
New volume = 0.9L × 0.8B × 1.05H
New volume = 0.756 × L × B × H
Percentage change in volume = ((New volume - Original volume) / Original volume) × 100
Percentage change = ((0.756 - 1) × 100) = -24.4%
Thus, the volume decreases by 24.4%.
हिन्दी उत्तर:
मान लीजिए कमरे की लंबाई, चौड़ाई और ऊँचाई क्रमशः L, B और H हैं।
मूल आयतन = L × B × H
परिवर्तन के बाद:
नई लंबाई = L - 10% of L = 0.9L
नई चौड़ाई = B - 20% of B = 0.8B
नई ऊँचाई = H + 5% of H = 1.05H
नया आयतन = 0.9L × 0.8B × 1.05H
नया आयतन = 0.756 × L × B × H
आयतन में प्रतिशत परिवर्तन = ((नया आयतन - मूल आयतन) / मूल आयतन) × 100
प्रतिशत परिवर्तन = ((0.756 - 1) × 100) = -24.4%
इस प्रकार, आयतन में 24.4% की कमी हुई है।