Arithmetic

Percentages

Easy

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

Entered answer:

✅ Correct Answer: 80

We have a chain of percentage relationships between four students' scores:

A scored 10% less than B

B scored 25% more than C

C scored 20% less than D

A's actual score = 72

We need to find D's score.

Instead of setting up complex algebraic equations, we'll use a proportional method. This works because percentages create fixed ratios between the scores.

Key Insight: We can assume any convenient value for one person's score, find the others proportionally, then scale everything to match A's actual score of 72.

Let's assume D's score = 100

Why 100? Because percentage calculations become super easy when working with 100 as a base.

Finding C's score:

C scored 20% less than D

C = D - 20% of D = 100 - 20 = 80

Finding B's score:

B scored 25% more than C

B = C + 25% of C = 80 + (25% × 80) = 80 + 20 = 100

Finding A's score:

A scored 10% less than B

A = B - 10% of B = 100 - (10% × 100) = 100 - 10 = 90

In our assumed scenario:

When A scores 90, D scores 100

In reality:

A actually scored 72

So we need to find: If A scores 72 instead of 90, what does D score?

We can set up a simple proportion:

$\tfrac{\text{A's assumed score}}{\text{D's assumed score}} = \tfrac{\text{A's actual score}}{\text{D's actual score}}$

$\tfrac{90}{100} = \tfrac{72}{D}$

Cross multiply:

$90 \times D = 72 \times 100$

$90D = 7200$

$D = \tfrac{7200}{90} = 80$

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CAT Past Year Questions (Topic-Wise)

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