Mathematics: Field Mensuration, Inputs and Percentage Reasoning
Mathematics here is arithmetic and mensuration applied to field and input problems.
Core areas
- Percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, time and distance, mixtures and partnership.
- Mensuration: area of rectangle, square, triangle, circle and trapezium; volume of cuboid and cylinder.
- Conversions: 1 hectare = 10,000 square metres = 2.47 acres; 1 quintal = 100 kg; 1 tonne = 1,000 kg; 1 cubic metre = 1,000 litres.
Approach
Write the given quantities with their units, convert everything to one unit, then substitute. For any percentage change, the original value is the base.
Worked example
A rectangular field is 150 m by 90 m. Area = 150 multiplied by 90 = 13,500 square metres, which is 1.35 hectares. At a wheat seed rate of 100 kg per hectare, seed needed = 1.35 multiplied by 100 = 135 kg. If seed costs 45 rupees per kg, the cost is 135 multiplied by 45 = 6,075 rupees. If only 1.2 ha is actually sown, the shortfall is 13,500 minus 12,000 = 1,500 square metres, equal to 15 kg of seed.
Second quick check
Average of 40, 45, 50 and 65 = 200 divided by 4 = 50. Adding a fifth value of 60 gives 260 divided by 5 = 52, so the average rises by 2. Questions of the type by how much does the average change are common.
Traps
- Converting 20 cm to 0.02 m instead of 0.2 m.
- Using the new value rather than the original as the base in percentage questions.
- Ignoring units in mensuration; area in square metres and length in metres must not be mixed.
- A village bigha differs by region; use hectares unless the question defines the local unit.