Dyarchy system was first introduced in the Act of 1919. Dyarchy was system of double government that was introduced by British Government in India. It was first introduced in the government of India Act, 1919. The principle of dyarchy was a division of the executive branch of each provincial government into authoritarian and popularly responsible sections.
The first was composed of executive councilors, appointed, as before, by the crown. The second was composed of ministers who were chosen by the governor from the elected members of the provincial legislature. These latter ministers were Indians.
Different fields and work of administration were divided between ministers and councilors. The dyarchy system was abolished with the introduction of provision of autonomy in the government of India Act 1935. You can read more about Dyarch here.
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