Question

Mass fractions of carbohydrate, protein, fat, ash, and water in banana are 0.220, 0.010, 0.005, 0.015, and 0.750, respectively. The density of carbohydrate, protein, fat, ash, and water are 1550, 1220, 900, 610, and 1000 \(kg.m^{-3}\), respectively. The density of banana, in \(kg.m^{-3}\), is nearest to

• A. 1116.85
• B. 1056.05
• C. 1000.00
• D. 1107.70

Hint:

Multiply each component's mass fraction by its own density and add all five contributions.

Answer 1

The Correct Option is A

Step 1: Set up the mass fraction weighted density model.
For a mixture where the composition is given as mass fractions, the bulk density is found from \( \rho = \sum x_i \rho_i \), summing each component's mass fraction times its own density.

Step 2: Multiply each mass fraction by its density.
Carbohydrate: \( 0.220 \times 1550 = 341.0 \).
Protein: \( 0.010 \times 1220 = 12.2 \).
Fat: \( 0.005 \times 900 = 4.5 \).
Ash: \( 0.015 \times 610 = 9.15 \).
Water: \( 0.750 \times 1000 = 750.0 \).

Step 3: Add the contributions.
\( \rho = 341.0 + 12.2 + 4.5 + 9.15 + 750.0 = 1116.85\ kg.m^{-3} \).

Final Answer:
The density of banana comes out to 1116.85 kg per cubic metre, matching option (A). \[ \boxed{\rho \approx 1116.85\ kg.m^{-3}} \]