The cost of 5 kg apples and 3 kg oranges is ₹535. If the cost of 8 kg apples and 6 kg oranges is ₹910, then what is the cost of 2 kg apples and 8 kg oranges?

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Accepted Answer

1. **Define variables**:  
   - Let the cost of 1 kg of oranges = ₹x.  
   - Let the cost of 1 kg of apples = ₹y.

2. **Form equations from the given data**:  
   - From the first condition:  
     $$5y + 3x = 535$$.  
   - From the second condition:  
     $$8y + 6x = 910$$.

3. **Simplify the second equation**:  
   Divide through by 2:  
   $$4y + 3x = 455$$.

4. **Eliminate one variable**:  
   Subtract the simplified second equation from the first equation:  
   $$
   (5y + 3x) - (4y + 3x) = 535 - 455.
   $$  
   Simplify:  
   $$y = 80$$.

5. **Find x using one equation**:  
   Substitute $$y = 80$$ into $$4y + 3x = 455$$:  
   $$
   4(80) + 3x = 455.
   $$  
   Simplify:  
   $$
   320 + 3x = 455 \implies 3x = 135 \implies x = 45.
   $$

6. **Calculate the required cost**:  
   Cost of 2 kg apples and 8 kg oranges = $$2y + 8x$$:  
   $$
   (2 	imes 80) + (8 	imes 45) = 160 + 360 = ₹520.
   $$

Thus, the cost of 2 kg apples and 8 kg oranges is **₹520**, and the correct answer is **(c)**.

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