Valmiki Ramayana Yuddha Kanda Sarga 129 Shloka 47
Original Shlokaश्रुत्वातांमैथिलींरामस्त्वाशशंसे च जीवितम् ।।6.129.47।। जीवितान्तमनुप्राप्तःपीत्वामृतमिवातुरः ।
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रामस्तु Rama also, तांमैथिलीम् about Mythili, श्रुत्वा hearing, जीवितान्तम् end of life, अनुप्राप्तः having heard of Mythili, आतुरः ailing man, अमृतम् nectar, पीत्वेव as if drunk, जीवितम् life, आशशंसे regained hope of life
"Just as an ailing man at the end of life regains hope on drinking nectar, Sri Rama also gains hope on hearing about Mythili."