Multiple choice

Passage

Directions: Read the data given below carefully and answer the question. The data shows the volume and dimensions (length, breadth, and height) of four cuboidal tanks: A, B, C, and D. The data also depicts the time taken to fill or empty the tanks by inlet pipes X, Y, and the outlet pipe Z. 1. The breadth of tank D is 14 m. Tank Data: Tank Volume (m³) Dimensions: L × B × H (m) Time taken by pipe X to fill (hours) Ratio of time taken by pipe Y to fill and pipe Z to empty A 3,600 20 × 15 × ---- 10 2 : 3 B ----- 25 × 12 × 12 3 : 2 C 4,500 ---- × 6 × 15 18 1 : 4 D 16,800 14 × ---- × ---- ----- 3 : 5

Find the respective ratio of the lateral surface area of tank A to the total surface area of tank C.

  1. 5 : 4

  2. 2 : 5

  3. 7 : 15

  4. 7 : 19

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Lateral surface area of tank A (20x15xH) = 2*H*(20+15) = 70H. Volume = 3600 = 20*15*H, so H = 12. LSA = 70*12 = 840. Total surface area of C (L*6*15) = 2*(6L + 90 + 15L) = 2*(21L + 90). Volume = 4500 = L*6*15, so L = 50. TSA = 2*(21*50 + 90) = 2*(1050 + 90) = 2280. Ratio = 840 / 2280 = 84 / 228 = 7 / 19.

AI explanation

For tank A, the height is found by dividing the volume by the base area: 3600 / (20 * 15) = 12 m. The lateral surface area of tank A is 2 * (length + breadth) * height = 2 * (20 + 15) * 12 = 840 sq m. For tank C, the length is found by dividing the volume by the base area: 4500 / (6 * 15) = 50 m. The total surface area of tank C is 2 * (lb + bh + hl) = 2 * (50 * 6 + 6 * 15 + 15 * 50) = 2 * (300 + 90 + 750) = 2280 sq m. The required ratio is 840 : 2280, which simplifies by dividing both sides by 120 to get 7 : 19.

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