Question

One say "Give me a hundred, friend ! I shall then became twice as rich as you." The other replies ,"If you give me ten, I shall be six times as rich as you". Tell me what is the amount of their (respective) capital ? [From the Bijaganita of Bhaskara 2] [ Hint : (x+ 100), y+10=6(x-10)].

Answer 1

Let one friend has capital amount= ₹ x and other friend has capital amount =₹ y .ATQx + 100 = 2(y − 100)x + 100 = 2y − 200x - 2y = -200 -100x − 2y = −300……………….(1)and 6(x − 10) = (y + 10)6x − 60 = y + 106x - y = 10 +606x − y = 70…………………….(2)By using elimination methodOn Multiplying equ (2) by 2,12x − 2y = 140……………….(3)On Subtracting equation (1) from equation (3),12x − 2y - (x − 2y ) = 140 - (-300)12x - 2y - x + 2y = 140 + 300)11x = 140 + 30011x = 440x = 440/11x = 40Put x = 40 in equation (1),x − 2y = −30040 − 2y = −30040 + 300 = 2y2y = 340y = 340/2y = 170Hence, the amount of first friend capital is ₹ 40 and the amount of second friend capital is ₹ 170.
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Answer 2

Answer:

hey mate..

your answer is in the above attachment...

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