One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six tim

Question

One says, “Give me a hundred, friend! I shall then become 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 II)

[ Hint: x + 100 = 2 (y – 100) , y + 10 = 6 ( x – 10 ) ]​

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Isabelle 1 month 2021-08-14T20:40:25+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-14T20:41:32+00:00

    Solution :

    ✪ Let the amount of capital with first person be x

    ✪ Now, let the amount of capital with second person be y

    According to the first condition

    ✒Second person gives Rs.100 to first person

    • The amount of the 1st person = x + 100
    • The amount of the 2nd person = y-100

    → (x + 100) = 2(y – 100)

    → x + 100 = 2y – 200

    → x – 2y = – 100 – 200

    → (x – 2y) = – 300 (i)

    According to the second condition

    ✒First person gives Rs.10 to second person

    • The amount of the 1st person = x – 10
    • The amount of the 2nd person = y+10

    → 6(x – 10) = y + 10

    → 6x – 60 = y + 10

    → 6x – y = 60 + 10

    → (6x – y) = 70 (ii)

    Multiply (i) by 1 and (ii) by 2

    • x – 2y = -300
    • 12x – 2y = 140

    Subtract both the equations

    → (x – 2y) – (12x – 2y) = -300 – 140

    → x – 2y – 12x + 2y = – 440

    → -11x = – 440

    → x = 440/11 = 40

    Putting the value of x in equation (i)

    → x – 2y = -300

    → 40 – 2y = – 300

    → – 2y = -300 – 40

    → – 2y = – 340

    → y = 340/2 = 170

    Hence,

    • The amount of capital with first person = x = Rs.40
    • The amount of capital with second person = y = Rs.170
    0
    2021-08-14T20:42:03+00:00

    \huge\underline{\overline{\mid{\bold{ \orange{Given}}\mid}}}

    • One man says Give me a hundred freind
    • and saying i will become twice rich than you
    • the other man replies if you give me ten i shall give be six times rich as you

    \huge\underline{\overline{\mid{\bold{ \red{To \:  Find}}\mid}}}

    • What is the amount of their ( respective capital )
    • (From the Bijaganita of Bhaskara II)

    \huge\underline{\overline{\mid{\bold{ \blue{Solution}}\mid}}}

    Let those friends were having Rs x and y with them.

    Using the information given in the question, we obtain

    ➠ x + 100 = 2 (y – 100)

    ➠ x + 100 = 2y – 200

    ➠ x – 2y = -300 (i)

    ➠ And, 6 (x – 10) = (y + 10)

    ➠ 6x – 60 = y + 10

    ➠ 6x – y = 70 (ii)

    Multiplying equation (ii) by 2, we obtain

    12x – 2y = 140 (iii)

    Subtracting equation (i) from equation (iii), we obtain

    ➠ 11x = 140 + 300

    ➠ 11x = 440

    ➠ x = 40

    Using this in equation (i), we obtain

    ➠ 40 – 2y = -300

    ➠ 40 + 300 = 2y

    ➠ 2y = 340

    ➠ y = 170

    Therefore, those friends had Rs 40 and Rs 170 with them respectively.

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