ICAR AIEEA PG Agri-Business Management 14 July 2023 (Shift 1) Paper

Partnership profit distribution:

• Total profit = Rs. 880.
• Raj's management commission ($12.5\% = \frac{1}{8}$):
  $\text{Management fee} = 880 \times 0.125 = \text{Rs. } 110$.
• Remaining divisible profit:
  $880 - 110 = \text{Rs. } 770$.
• Capital ratio (Raj : Sanjay) = $5000 : 6000 = 5 : 6$.
  Total parts = $5 + 6 = 11$.
  Raj's share of remaining profit = $\frac{5}{11} \times 770 = 5 \times 70 = \text{Rs. } 350$.
• Raj's total earnings:
  $\text{Total share} = 110 + 350 = 460\text{ INR}$.
  
  Option analysis:
• INR 470: Calculation error.
• INR 465: Calculation error.
• INR 460: Correct total share for Raj.
• INR 455: Calculation error.

Volume calculation of rectangular hall:

• Dimensions: Length $L = 15\text{ m}$, Breadth $B = 12\text{ m}$, Height $H$.
• Floor area = $15 \times 12 = 180\text{ m}^2$.
  Ceiling area = $15 \times 12 = 180\text{ m}^2$.
  Sum of floor and ceiling areas = $180 + 180 = 360\text{ m}^2$.
• Area of four walls = $2(L + B)H = 2(15 + 12)H = 2(27)H = 54H$.
• Setting areas equal:
  $54H = 360 \implies H = \frac{360}{54} = \frac{20}{3}\text{ m}$.
• Volume of hall:
  $V = L \times B \times H = 15 \times 12 \times \frac{20}{3} = 180 \times \frac{20}{3} = 60 \times 20 = 1200\text{ m}^3$.
  
  Option analysis:
• 720: Calculation error.
• 900: Calculation error.
• 1200: Correct volume in cubic meters.
• 1800: Calculated as $180 \times 10$.

Verification of statements:

• Statement I:
  State A Undergraduate = $28\% \text{ of } 55750 = 0.28 \times 55750 = 15610$.
  State B Undergraduate = $40\% \text{ of } 86500 = 0.40 \times 86500 = 34600$.
  Total Undergraduate = $15610 + 34600 = 50210$. -> True.
• Statement II:
  State A Ph.D = $8\% \text{ of } 55750 = 4460$.
  State B Ph.D = $10\% \text{ of } 86500 = 8650$.
  Ratio = $\frac{4460}{8650} \approx 0.5156 \neq 0.75$. -> False.
• Statement III:
  Difference = $8650 - 4460 = 4190 \neq 3690$. -> False.