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24 June, 06:37

Two kg of tea and 3 kg of sugar cost rupees 39 in january 1997, However in march 1997 the price of the tea increased by 25% and the price of the sugar increased by 20% and the same quantity of tea and sugar cost rupees 48.30. Find their prices in January

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Answers (2)
  1. 24 June, 10:14
    0
    Answer: tea = 15 rupees per kg

    sugar = 3 rupees per kg

    Step-by-step explanation:

    Hi, to answer this question we have to write a system of equations with the information given:

    "Two kg of tea and 3 kg of sugar cost rupees 39 in january 1997":

    2 t + 3 s = 39 (a)

    Where:

    t = price of 1 kg of tea s = price of 1 kg of sugar

    "in march 1997 the price of the tea increased by 25% (1.25) and the price of the sugar increased by 20% (1.20) and the same quantity of tea and sugar cost rupees 48.30. "

    2 (t1.25) + 3 (s1.2) = 48.30 (b)

    Solving for t in (b)

    2t = 39-3s

    t = (39 - 3s) / 2

    t = 19.5-1.5s

    Replacing the value of t in (b)

    2 x ((19.5-1.5s) 1.25) + 3 (1.2s) = 48.30

    2x (24.375 - 1.875s) + 3.6s = 48.30

    48.75 - 3.75s+3.6s = 48.30

    48.75-48.30 = 3.75s-3.6s

    0.45 = 0.15s

    0.45/0.15 = s

    3 = s

    Replacing the value of s in (a)

    2 t + 3 (3) = 39

    2 t + 9 = 39

    2 t = 39 - 9

    2 t = 30

    t = 30/2

    t = 15

    Prices in january:

    tea = 15 rupees per kg

    sugar = 3 rupees per kg

    Feel free to ask for more if needed or if you did not understand something.
  2. 24 June, 10:26
    0
    x = 15 rupees by kg (price of tea)

    y = 3 rupees by kg (price of sugar)

    Step-by-step explanation:

    Let call " x " the price of kg of tea and " y " the price of kg of sugar, in january of 1997,

    then according to problem statement

    2*x + 3*y = 39 (1)

    But in march prices increased

    tea by 25% that means its price in march will be 1.25*x, and the price of sugar will be 1.20*y, finally buying the same quantities now cost 48.30 rupees, then

    2 * (1.25*x) + 3 * (1.20*y) = 48.30

    2,50*x + 3.60*y = 48.30 (2)

    Equations (1) and (2) are a two equation system, we need to solve for x and y

    From equation (1) we have y = (39 - 2*x) / 3

    Plugging that value in equation (2)

    2,50*x + 3.60 * [ (39 - 2*x) / 3] = 48.30

    2,50*x + (140,40 - 7,20*x) / 3 = 48.30

    7.50*x + 140,40 - 7,20*x = 144,90

    0,30*x = 4.50

    x = 4.50/0.30

    x = 15 rupees

    and y = (39 - 2*x) / 3 ⇒ y = (39 - 2*15) / 3

    y = (39 - 30) / 3

    y = 3 rupees
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