The Geography of North India causes all rivers to drain into the Indus river, and then into the Arabian Sea. Mansarovar in Tibet (called Swarga, whose town Amravati was the capital of Indra, the leader of the Aryans) has two outlets. It bears BrahmaPutra in the east and Indus in the west, both of which border the subcontinent and drain the Himalayas, along with their numerous snow-fed tributaries. Millenia ago, Indus drained North India and Pakistan along with its tributaries : Jhelum(Vitasta), Chenab(Chandrabhaga), Ravi(Irawati), Sutlej(Satradru), Beas(Bipasha), Saraswati (since gone underground in Haryana), and Ganga!!! As seen from the map below, the beginning of the Ganga is almost parallel to Sutlej. Yes, thanks to the topography of North India, Ganga flowed Westwards.
The vast plain of India was called Prithvi or earth, which was the reclaimed trough land from the Tethys Sea or Ksheer Sagar, and it lay between the mighty Himalayas and the tall Vindhyas. This plain lacked any snow-fed river, and hence, a constant supply of clean drinking water was never available. Water-borne diseases were rampant, e.g. jaundice (curse of the yellow-skinned Kapil Muni). Thousands succumbed to it, making Anga and Banga (Bihar and Bengal) uninhabitable.
The King of the plains (King Sagar) foresaw the need of a snow-fed river for year-long uninterrupted supply of fresh clean water for the population. He decided, planned, sponsored, and executed a huge civil engineering project, to divert the Ganga (the eastern-most tributary of Indus); into the plain eastwards, to meet Brahmaputra (in Bangladesh). This project employed 60,000 skilled and unskilled workers, and took a few decades to be completed. By then, Sagar's grandson, Bhagirath, had already ascended the throne.
The point of divertion, which involved almost a 90 degree bend of the river-bed, lay in Gaumukh, the snow-capped culmination of the Gangotri Glacier. Gangotri = Ganga + Uttari (Northern). This means, the Ganga flows northerly (actually north-westerly) here. This is where the descending water was temporarily held, before the rest of the downstream easterly canal was ready to be drained. (Ganga was temporarily held in Shiva's matted hair during her journey to the earth). King Bhagiratha opened the Gaumukh lockgates to drain the 2500 km long canal with the fresh, clean, inexhaustible supply of water. The states of Uttarakhand, Uttar Pradesh, Bihar, Bengal, and the country of Bangladesh, were 'purified'. The water-borne epidemics subsided in Banga (Kapil Muni's curse ended), making it inhabitable, which later cradled the Bengali culture.
As seen in the map of Ganga below, the river is equidistant from the Himalayas and the Vindhyas. It was planned to be dug in this manner by King Sagar, in order to equally drain both the sides. After the water of the huge Ganga was diverted, tributaries from the snow-fed Himalayas and rain-fed Vindhyas joined her and drained the Indo-Gangetic plain with alluvial soil, making it the most fertile plain in the world, and the grain bowl of India. Agriculture flourished : Rice, wheat, jowar, bajra, ragi, sugarcane, jute, pulses, vegetables, mango, guava, flooded the sub-continent and the neighbouring countries. Economic security swelled the population here : Uttar Pradesh and Bihar are the most populus states even today. This river sustained the whole population and hence, was personified as a Mother (life-giver) or a Goddess (source of a blessing). If this rich plain is cultivated to its full capacity, it can feed the whole world.
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P.S. : Vindhyas are also fold mountains like Himalayas. In a certain prehistoric age, the tectonic movements caused the Vindhyas to rise in altitude at a very fast rate. However, the process subsided within a few centuries, and the highest peak in the Vindhyas is only 1048m (Amarkantak, the source of River Narmada).