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CAT 2019Slot 2QAQuestion & Solution

ArithmeticEasy

Question

In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was

Solution

1. Concept Used

  • Topic: Percentage — Chain Relationship between variables
  • Formula: $$\text{New Value} = \text{Original Value} \times \left(1 \pm \frac{\text{percentage}}{100}\right)$$

2. Calculation

Let the score of D be denoted as $$d$$.

Step 1: Score of C C scored 20% less than D: $$C = d \times \left(1 - \frac{20}{100}\right) = d \times \frac{80}{100} = 0.8d$$

Step 2: Score of B B scored 25% more than C: $$B = 0.8d \times \left(1 + \frac{25}{100}\right) = 0.8d \times \frac{125}{100} = 0.8d \times 1.25 = d$$

Step 3: Score of A A scored 10% less than B: $$A = d \times \left(1 - \frac{10}{100}\right) = d \times \frac{90}{100} = 0.9d$$

Step 4: Solve for d Given that A scored 72: $$0.9d = 72$$ $$d = \frac{72}{0.9} = \frac{72 \times 100}{90} = \frac{7200}{90} = 80$$

3. Solution

Answer = 80 ✅

The final calculated score of D is 80.