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Let's analyze the problem step-by-step.

### Given:
- Total amount: Rs 1300
- Initial ratio of division among 3 students \(X : Y : Z = 2 : 4 : 7\)
- Revised ratio to be considered \(1/2 : 1/4 : 1/7\)

We need to find out who gains the most under the revised ratio and by how much.

### Step 1: Calculate the actual amounts received by X, Y, and Z in the original ratio

The total parts of the ratio \(2 + 4 + 7 = 13\).

- Amount received by \(X = \frac{2}{13} \times 1300 = 200 \text{ Rs}\)
- Amount received by \(Y = \frac{4}{13} \times 1300 = 400 \text{ Rs}\)
- Amount received by \(Z = \frac{7}{13} \times 1300 = 700 \text{ Rs}\)

### Step 2: Calculate the revised ratio

The revised ratio \(1/2 : 1/4 : 1/7\):
- Find a common factor to convert the fractions into integer values.
  
The least common multiple (LCM) of 2, 4, and 7 is 28. Converting the fractions:
- \(1/2 = 14/28\)
- \(1/4 = 7/28\)
- \(1/7 = 4/28\)

Thus, the new ratio is \(14 : 7 : 4\).

### Step 3: Calculate the actual amounts received under the revised ratio

The total parts of the revised ratio \(14 + 7 + 4 = 25\).

- Amount received by \(X = \frac{14}{25} \times 1300 = 728 \text{ Rs}\)
- Amount received by \(Y = \frac{7}{25} \times 1300 = 364 \text{ Rs}\)
- Amount received by \(Z = \frac{4}{25} \times 1300 = 208 \text{ Rs}\)

### Step 4: Determine who gains the most and by how much

Let's compare:
- \(X\) originally got 200 Rs but now gets 728 Rs, gaining \(728 - 200 = 528 \text{ Rs}\)
- \(Y\) originally got 400 Rs but now gets 364 Rs, losing \(400 - 364 = 36 \text{ Rs}\)
- \(Z\) originally got 700 Rs but now gets 208 Rs, losing \(700 - 208 = 492 \text{ Rs}\)

**The student \(X\) gains the most with an additional Rs 528.**

### Final Answer:
**(a) X, Rs 528**

Would you like more details or explanations on any step?

### Relative Questions:
1. How do you find the LCM of numbers to convert fractions into a ratio?
2. Why does the total of the ratio parts matter when dividing an amount?
3. How can you convert fractional ratios into whole-number ratios?
4. What is the significance of the total amount when distributing in ratios?
5. How can ratios be simplified to their smallest terms?

### Tip:
Always convert ratios involving fractions to whole numbers using the least common multiple (LCM) to make calculations easier.

Rs 1300 was divided among 3 students in the ratio 2:4:7. Had it been divided in the ratio 1/2:1/4:1/7, who would have gained the most and how much?

Explore how the distribution of Rs 1300 among three students changes when the division ratio is altered from 2:4:7 to 1/2:1/4:1/7. Learn which student gains the most and by how much, using basic arithmetic and ratio concepts.

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