The thresher of a wheat combine harvester has an optimal throughput capacity of 2400 kg (crop) per hour. The harvester has a forward velocity of 4.5 km h−1. Sample tests have revealed that the yield of crop in the field is 3000 kg (grain) per ha. Grain to straw ratio is 60 : 40. If the above throughput is to be maintained, the width of cut of the harvester in m, neglecting turning losses, is
GATE AG - 2012,
Answer: B
The width of cut is about 1.07 m.
The thresher capacity is in kg of crop (grain plus straw), while the yield is given in kg of grain. With a grain to straw ratio of 60 : 40, each hectare carries 3000/0.6 = 5000 kg of crop:
\[ \begin{aligned} \text{area rate} &= \frac{2400\ \text{kg/h}}{5000\ \text{kg/ha}} = 0.48\ \text{ha/h} \\ &= 4800\ \text{m}^{2}/\text{h} \\ w &= \frac{4800}{4500\ \text{m/h}} = 1.07\ \text{m} \end{aligned} \]
Treating the 2400 kg/h as grain gives 0.8 ha/h and a width of 1.78 m, which is the trap in this question. The other widths do not correspond to the crop throughput at 4.5 km/h.
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