Question

Rs. 8400 are divided among A, B, C and D in such a way that the shares of A and B, B and C as well as C and D are in the ratios of 2 : 3, 4 : 5 and 6 : 7 respectively. Determine the share of A?

• A. Rs. 1020
• B. Rs. 1280
• C. Rs. 8450
• D. Rs. 4200
• E. Rs. 1320

Hint:

To combine ratios, find a common term (like (b) and make it equal in both ratios.

Answer 1

The Correct Option is B

Step 1: Let A:B = 2:3, B:C = 4:5, C:D = 6:7.
Step 2: Make the ratios continuous. Multiply to get common B: A:B = 2:3 = 8:12 (multiply by 4). B:C = 4:5 = 12:15 (multiply by 3). So A:B:C = 8:12:15.
Step 3: Now C:D = 6:7. C is 15 in A:B:C. Multiply C:D to have C=15: 6:7 = 15:17.5 (multiply by 2.5). So A:B:C:D = 8:12:15:17.5.
Step 4: Multiply by 2 to avoid decimals: 16:24:30:35.
Step 5: Total parts = $16 + 24 + 30 + 35 = 105$.
Step 6: A's share = $\frac{16}{105} \times 8400 = 16 \times 80 = 1280$.
Step 7: Final Answer: Rs. 1280.