7. A goat consumes 2 kg of grass per day, and a cow consumes 4 kg of grass per day.
Two pairs of goats and one pair of cattle are released in a sanctuary with a total biomass
of 16,000 kg of grass at the time of release. The growth rate of grass accounts for an
increase of 1000 kg every 100 days. How much grass stands after 1000 days?
a. 100 kg
b. 500 kg
c. 1,000 kg
d. 10,000 kg
Grass Biomass Calculation: Goats, Cows, and Growth Rates
Two pairs of goats (4 goats) and one pair of cattle (2 cows) consume grass in a sanctuary starting with 16,000 kg biomass, where grass grows by 1,000 kg every 100 days. After 1000 days, 10,000 kg of grass remains [execute_python].
Detailed Solution
Initial biomass stands at 16,000 kg. Four goats consume 8 kg daily (4 × 2 kg), and two cows consume 8 kg daily (2 × 4 kg), totaling 16 kg consumed per day.
Grass growth rate equals 10 kg per day (1,000 kg / 100 days). Net daily depletion becomes 6 kg (16 kg consumed – 10 kg growth).
Over 1000 days, total net consumption equals 6,000 kg (6 kg/day × 1000 days). Remaining grass calculates as 16,000 kg – 6,000 kg = 10,000 kg.
Option Analysis
Option a: 100 kg
This underestimates remaining biomass. Simple total consumption without growth (16 kg/day × 1000 = 16,000 kg) depletes exactly to zero, but growth adds 10,000 kg total (10 kg/day × 1000), leaving far more than 100 kg.
Option b: 500 kg
Ignores full growth impact. Partial accounting, like growth over fewer periods or miscalculated animals, might suggest this, but precise daily netting confirms 10,000 kg remains.
Option c: 1,000 kg
Matches one growth cycle but overlooks compounding over 10 cycles (1000 kg × 10). Daily precision shows sustained net loss of 6 kg/day yields 10,000 kg.
Option d: 10,000 kg (Correct)
Accounts for initial stock minus net depletion: 16,000 – (16-10)×1000 = 10,000 kg, aligning with steady-state growth-consumption dynamics [execute_python].
In competitive exams like CSIR NET Life Sciences, the goat cow grass consumption sanctuary biomass calculation tests ecological modeling and rates. This problem features two pairs of goats (4 goats at 2 kg/day each), one pair of cattle (2 cows at 4 kg/day each), initial 16,000 kg grass, and 1,000 kg growth every 100 days—querying biomass after 1000 days.
Daily intake totals 16 kg, offset by 10 kg/day growth, netting 6 kg/day loss. From 16,000 kg start, 1000 days deplete 6,000 kg, leaving 10,000 kg—option d [execute_python].
Such problems mimic grassland carrying capacity, relevant to ecology and environmental biology. Practice reveals patterns: steady growth assumes linear rates, ignoring limits like overgrazing thresholds seen in real studies. For CSIR NET aspirants, master these via net rate formulas: Final = Initial + (Growth – Consumption) × Time.
