Question

A dishonest dealer professes to sell his goods at the cost price but uses a false weight and thus gains 25%. How much quantity of grains does he give for a kilogram?

• A. 900 grams
• B. 750 grams
• C. 975 grams
• D. 800 grams

Answer 1

Answer:

D. 800 grams

The dishonest dealer gives 800 grams of grains for a kilogram.

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• Understand the Gain Formula:
  When a dealer sells goods at cost price but uses a false weight, the profit percentage is calculated as:
  $\text{Gain \%} = \left( \frac{\text{True Weight} - \text{False Weight}}{\text{False Weight}} \right) \times 100$

• Identify the Given Values:

  • True Weight = $1\text{ kg} = 1000\text{ grams}$

  • Gain % = $25\%$

  • Let the False Weight = $x\text{ grams}$

• Set up the Equation:
  $25 = \left( \frac{1000 - x}{x} \right) \times 100$

• Solve for $x$:

  • Divide both sides by $100$:
    $\frac{25}{100} = \frac{1000 - x}{x} \implies \frac{1}{4} = \frac{1000 - x}{x}$

  • Cross-multiply:
    $x = 4 \times (1000 - x)$

    $x = 4000 - 4x$

  • Rearrange and add $4x$ to both sides:
    $5x = 4000$
    $x = \frac{4000}{5} = \mathbf{800\text{ grams}}$

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Shortcut Method

• A profit of $25\%$ means a fraction increase of $\frac{1}{4}$.

  • This means for every $4$ parts he gives out, he charges the customer for $4 + 1 = 5$ parts.

  • Since $5\text{ parts} = 1000\text{ grams}$ (the true weight), then $1\text{ part} = 200\text{ grams}$.

  • The actual weight he gives out is $4\text{ parts} = 4 \times 200 = \mathbf{800\text{ grams}}$.