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      Question

      Sarla had Rs. 8000 in total. She spent x% of this amount on

      food. After that, she spent (x + 20)% of the remaining money on rent. Additionally, she spent Rs. 1920 on clubbing. The remaining amount, which she saved, is 31.25% of her initial amount. Based on this information, determine the value of x.
      A 10 Correct Answer Incorrect Answer
      B 20 Correct Answer Incorrect Answer
      C 15 Correct Answer Incorrect Answer
      D 30 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Amount saved by Sarla = 0.3125 × 8000 = Rs. 2500

      Amount spent on food = x/100 × 8000 = Rs. 80x

      Amount spent on rent = (x + 20)/100 × (8000 – 80x) = (x + 20)(80 – 0.8x)

      Or, 80x + (x + 20)(80 – 0.8x) = 8000 – 2500 – 1920 = 3580

      Or, 80x + 80x + 1600 – 0.8x 2  – 16x = 3580

      Or, 0.8x 2  – 144x + 1980 = 0

      Or, x 2  – 180x + 2475 = 0

      Or, x 2  – 165x – 15x + 2475 = 0

      Or, x(x – 165) – 15(x – 165) = 0

      Or, (x – 15)(x – 165) = 0

      Or, x = 15 [x = 165 is not possible]

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