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: List each component's mass fraction and density side by side.
Carbohydrate 0.220 at $1550\ kg/m^3$, protein 0.010 at $1220\ kg/m^3$, fat 0.005 at $900\ kg/m^3$, ash 0.015 at $610\ kg/m^3$, water 0.750 at $1000\ kg/m^3$.

Step 2: Check the fractions add to one.
$0.220+0.010+0.005+0.015+0.750 = 1.000$, so the composition is complete and no component is missing.

Step 3: Build a running sum of mass fraction times density.
After carbohydrate: $341.0$. After protein: $341.0+12.2=353.2$. After fat: $353.2+4.5=357.7$. After ash: $357.7+9.15=366.85$. After water: $366.85+750.0=1116.85$.

Step 4: Read the final density.
The running total finishes at $1116.85\ kg/m^3$, the mass fraction weighted density of the banana.

Final Answer:
Building the sum term by term still gives $1116.85\ kg/m^3$, so option (A) is correct. \[ \boxed{1116.85\ kg.m^{-3}} \]