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An increase of 20% in the price of sugar makes a housewife get 2 kg less for Rs. 144. What is the price of sugar before the increase?

Answer :

To solve this problem, we need to determine the original price of sugar before the price increase.

Let's break it down step by step:

  1. Understanding the Problem:

    • The housewife is spending Rs. 144 on sugar.
    • Because of a 20% price increase, she now gets 2 kg less sugar for the same amount of money.

  2. Setting Up the Equation:

    • Let the original price per kg of sugar be Rs. [tex]x[/tex].
    • After a 20% increase, the new price per kg is [tex]x + 0.2x = 1.2x[/tex].

  3. Creating the Equation:

    • Originally, the quantity of sugar bought for Rs. 144 is [tex]\frac{144}{x}[/tex] kg.
    • After the increase, the quantity of sugar is [tex]\frac{144}{1.2x}[/tex] kg.

    According to the problem, the new quantity is 2 kg less than the original quantity:
    [tex]\frac{144}{x} - \frac{144}{1.2x} = 2[/tex]

  4. Solving the Equation:

    • Simplify and solve for [tex]x[/tex]:
      [tex]\frac{144}{x} - \frac{120}{x} = 2[/tex]
    • Combine the fractions:
      [tex]\frac{24}{x} = 2[/tex]
    • Solving for [tex]x[/tex], we find:
      [tex]24 = 2x[/tex]
      [tex]x = 12[/tex]

  5. Conclusion:

    • The original price per kg of sugar before the price increase was Rs. 12.

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Rewritten by : Barada