In his will, a man divided half his wealth among his sons Ravi and Shashi in the ratio 3 : 5 and the remaining half among his daughters Chitra and Devi in the ratio 7 : 9. If Chitra got Rs 6000 more than one of her brothers, then how much (in rupees) did Shashi get?

To solve the problem, let's break it down step by step:

1. **Let the total wealth be \( W \).**  
   The man divided half of his wealth among his sons Ravi and Shashi and the remaining half among his daughters Chitra and Devi.

2. **Division among the sons:**
   - The half of the wealth given to the sons is \( \frac{W}{2} \).
   - This is divided in the ratio 3:5.
   - Let the amounts received by Ravi and Shashi be \( 3x \) and \( 5x \) respectively.
   - Therefore, \( 3x + 5x = \frac{W}{2} \).
   - Simplifying gives \( 8x = \frac{W}{2} \), so \( x = \frac{W}{16} \).
   - Thus, Ravi gets \( 3x = \frac{3W}{16} \) and Shashi gets \( 5x = \frac{5W}{16} \).

3. **Division among the daughters:**
   - The other half of the wealth \( \frac{W}{2} \) is divided between Chitra and Devi in the ratio 7:9.
   - Let the amounts received by Chitra and Devi be \( 7y \) and \( 9y \) respectively.
   - Therefore, \( 7y + 9y = \frac{W}{2} \).
   - Simplifying gives \( 16y = \frac{W}{2} \), so \( y = \frac{W}{32} \).
   - Thus, Chitra gets \( 7y = \frac{7W}{32} \) and Devi gets \( 9y = \frac{9W}{32} \).

4. **Condition given in the problem:**
   - It is given that Chitra got Rs 6000 more than one of her brothers.
   - Assume Chitra got Rs 6000 more than Ravi. Hence, \( \frac{7W}{32} = \frac{3W}{16} + 6000 \).

5. **Set up the equation and solve for \( W \):**
   \[
   \frac{7W}{32} = \frac{6W}{32} + 6000
   \]
   \[
   \frac{W}{32} = 6000
   \]
   \[
   W = 6000 \times 32 = 192000
   \]

6. **Calculate Shashi's share:**
   \[
   \text{Shashi's share} = \frac{5W}{16} = \frac{5 \times 192000}{16} = 60000
   \]

Thus, Shashi received **Rs 60,000**.

Would you like any more details or have any questions about this solution?

Here are 5 relative questions to expand your understanding:
1. How would the answer change if the ratio between Ravi and Shashi was 2:3?
2. What would be the impact on the solution if Chitra got Rs 6000 less than one of her brothers instead of more?
3. Can you derive the general formula for Shashi's share given any ratios?
4. How would you calculate Devi's share in this situation?
5. What if the total wealth was not divided equally between sons and daughters?

**Tip:** Always double-check the interpretation of ratio problems to ensure you are setting up the correct equations.

Learn how to solve a ratio problem involving the division of wealth among sons and daughters. This problem covers concepts of ratio and proportion, linear equations, and fractional division. Find out how to calculate shares using specific ratios and conditions. Suitable for students in Grades 7-9.

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