SSC & BANK EXAMS: QUANTITATIVE APTITUDE · PROFIT, LOSS & DISCOUNT

Same selling price, x% gain and x% loss

Two items sold at the same price, one at x% gain and one at x% loss: there is always a loss of x²/100 %.

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Worked examples

Example 1 · level 1

Priya sold two mobile phones for the same price. On one there was a gain of 10% and on the other a loss of 10%. What is the overall result?

  1. 1% loss
  2. 1% gain
  3. 2% loss
  4. No profit, no loss
Show solution
  1. Loss % = x²/100 = 100/100 = 1%.
  2. This is always a loss, whatever the selling price.

Answer: 1% loss

Example 2 · level 2

Vihaan sold two TV sets for the same price. On one there was a gain of 25% and on the other a loss of 25%. What is the overall result?

  1. 2.5% loss
  2. No profit, no loss
  3. 6.25% loss
  4. 6.25% gain
Show solution
  1. Loss % = x²/100 = 625/100 = 6.25%.
  2. This is always a loss, whatever the selling price.

Answer: 6.25% loss

Example 3 · level 3

Diya sold two scooters for ₹1,980 each, gaining 10% on one and losing 10% on the other. Find the overall loss in rupees.

Show solution
  1. CP₁ = 1,980 × 100/110 = ₹1,800.
  2. CP₂ = 1,980 × 100/90 = ₹2,200.
  3. Total CP = ₹4,000, total SP = ₹3,960.
  4. Loss = ₹40.

Answer: ₹40

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