Final answer:
The discharge at the canal head for the Kharif crop is 288 cumecs, and for the Rabi crop is 767.25 cumecs.
Step-by-step explanation:
Given that the Gross Command Area (GCA) of the irrigation canal is 1.20 lakh hectare and the Culturable Command Area (CCA) is 75% of the GCA, we can calculate the CCA as follows:
CCA = 75% x GCA
CCA = 75% x 1.20 lakh hectare
CCA = 0.75 x 1.20 lakh hectare
CCA = 0.9 lakh hectare
Now, we can calculate the intensities of irrigation for Kharif and Rabi crops:
Intensity of irrigation for Kharif crop = 40% of CCA
Intensity of irrigation for Kharif crop = 40% of 0.9 lakh hectare
Intensity of irrigation for Kharif crop = 0.40 x 0.9 lakh hectare
Intensity of irrigation for Kharif crop = 0.36 lakh hectare
Intensity of irrigation for Rabi crop = 55% of CCA
Intensity of irrigation for Rabi crop = 55% of 0.9 lakh hectare
Intensity of irrigation for Rabi crop = 0.55 x 0.9 lakh hectare
Intensity of irrigation for Rabi crop = 0.495 lakh hectare
Now, we can calculate the discharge at the canal head using the duties at the canal for Kharif and Rabi crops:
Discharge at canal head for Kharif crop = Duty x Intensity of irrigation for Kharif crop
Discharge at canal head for Kharif crop = 800 ha/cumecs x 0.36 lakh hectare
Discharge at canal head for Kharif crop = 800 x 0.36 lakh cumecs
Discharge at canal head for Kharif crop = 288 cumecs
Discharge at canal head for Rabi crop = Duty x Intensity of irrigation for Rabi crop
Discharge at canal head for Rabi crop = 1550 ha/cumecs x 0.495 lakh hectare
Discharge at canal head for Rabi crop = 1550 x 0.495 lakh cumecs
Discharge at canal head for Rabi crop = 767.25 cumecs
Therefore, the discharge at the canal head for Kharif crop is 288 cumecs and for Rabi crop is 767.25 cumecs.