An amount is divided among Deepak, Shivam, and Prashant. The amount received by Deepak is Rs. 40 more than 40\% of the total amount. Shivam receives Rs. 5 more than 25\% of the total amount, while Prashant receives 32\% of the total amount. What is the amount received by Shivam?

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Accepted Answer

**Solution:**

1. Let the total amount be $ x $.

2. According to the problem:
   - Deepak's amount = $$ 40\% \text{ of } x + 40 = 0.4x + 40 $$
   - Shivam's amount = $ $25\% \text{ of } x + 5 = 0.25x + 5$ $
   - Prashant's amount = $ $32\% \text{ of } x = 0.32x$ $

3. The sum of all amounts equals the total amount:
   $$
   (0.4x + 40) + (0.25x + 5) + 0.32x = x
   $$

4. Combine like terms:
   $$
   0.4x + 0.25x + 0.32x + 40 + 5 = x
   $$
   $$
   0.97x + 45 = x
   $$

5. Rearranging to find $ x $:
   $$
  $ x - 0.97x = 45 \ 
   0.03x = 45 \ 
   x = \frac{45}{0.03} = 1500$
   $$

6. Calculate Shivam's amount:
   $$
   0.25 \times 1500 + 5 = 375 + 5 = 380
   $$

**Answer:** Rs. 380

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