A sum of ₹5100 is divided amongst A, B, and C, such that the ratio of shares of A and B is 1:2, and the ratio of shares of B and C is 3:4. Find the sum of the shares of A and B.

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Accepted Answer

1. **Understand the given ratios**:  
   - The ratio of A to B is 1:2.  
   - The ratio of B to C is 3:4.

2. **Combine the ratios**:  
   To find the overall ratio of A, B, and C, express these ratios in terms of a common variable:  
   - Multiply the first ratio (A:B = 1:2) by 3 to align with the second ratio (B:C = 3:4):  
     $$ A:B = 3:6 $$.  
   - Now combine $$ B:C = 6:8 $$.  
   - The overall ratio becomes $$ A:B:C = 3:6:8 $$.

3. **Calculate the total parts**:  
   Total parts = $$ 3 + 6 + 8 = 17 $$.

4. **Determine the value of one part**:  
   Total sum = ₹5100.  
   Value of one part = $$ \frac{5100}{17} = 300 $$.

5. **Find the shares of A and B**:  
   - Share of A = $$ 3 	imes 300 = ₹900 $$.  
   - Share of B = $$ 6 	imes 300 = ₹1800 $$.  
   - Sum of shares of A and B = $$ ₹900 + ₹1800 = ₹2700 $$.

Thus, the correct answer is **(d) ₹2700**.

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