The incomes of A and B are in the ratio 5:3. The expenditures of A, B, and C are in the ratio 8:5:2. If C spends ₹2000 and B saves ₹700, then what amount does A save?

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Accepted Answer

### Step-by-Step Solution:

1. **Determine the expenditure of B and A using the given ratio:**  
   - Expenditures of A, B, and C are in the ratio 8:5:2.  
   - Given that C's expenditure is ₹2000, calculate the unit value of the ratio:  
     $$ 	ext{Unit value} = \frac{	ext{C's expenditure}}{	ext{Ratio of C}} = \frac{2000}{2} = 1000. $$

- B's expenditure = $$ 5 	imes 1000 = ₹5000. $$  
   - A's expenditure = $$ 8 	imes 1000 = ₹8000. $$

2. **Calculate B's income using savings information:**  
   - B saves ₹700, so B's income is:  
     $$ 	ext{B's income} = 	ext{B's expenditure} + 	ext{B's savings} = 5000 + 700 = ₹5700. $$

3. **Find A's income using the income ratio (5:3):**  
   - The ratio of incomes of A and B is 5:3. Let A's income be $$ x $$:  
     $$ \frac{x}{5700} = \frac{5}{3}. $$  
     Solve for $$ x $$:  
     $$ x = \frac{5}{3} 	imes 5700 = ₹9500. $$

4. **Calculate A's savings:**  
   - A's savings = A's income - A's expenditure:  
     $$ 	ext{A's savings} = 9500 - 8000 = ₹1500. $$

### Final Answer:  
A saves **₹1500**, corresponding to option **(a)**.

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