Jai scores `20%` higher than Raj in an exam who scores `30%` more than Rohit who scores `10%` less than Ravi. What percent of marks are scored by Jai as compared to Ravi?

Options

A. A)`117%`
B. B)`140.4%`
C. C)`90%`
D. D)`127.8%`

Answer

To solve the problem step-by-step, we will establish the relationships between the scores of Jai, Raj, Rohit, and Ravi based on the given percentages.

### Step 1: Define the Scores
Let's denote Ravi's score as \( R \).

### Step 2: Calculate Rohit's Score
Rohit scores 10% less than Ravi. Therefore, Rohit's score \( H \) can be calculated as:
\[ H = R - 0.1R = 0.9R \]

### Step 3: Calculate Raj's Score
Raj scores 30% more than Rohit. Therefore, Raj's score \( A \) can be calculated as:
\[ A = H + 0.3H = 1.3H = 1.3(0.9R) = 1.17R \]

### Step 4: Calculate Jai's Score
Jai scores 20% higher than Raj. Therefore, Jai's score \( J \) can be calculated as:
\[ J = A + 0.2A = 1.2A = 1.2(1.17R) = 1.404R \]

### Step 5: Calculate Percentage of Jai's Score Compared to Ravi's Score
Now we need to find out what percent of Ravi's score is Jai's score. This can be calculated using the formula:
\[ \text{Percentage} = \left( \frac{J}{R} \right) \times 100 \]
Substituting the value of \( J \):
\[ \text{Percentage} = \left( \frac{1.404R}{R} \right) \times 100 = 1.404 \times 100 = 140.4\% \]

### Conclusion
Jai scores **140.4%** of the marks compared to Ravi.

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