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: Understanding the Concept:
Merging individual ratios (A:B, B:C, C:D) into a single continuous ratio (A:B:C:D).
Step 2: Key Formula or Approach:
Equate the common terms across ratios.
Step 3: Detailed Explanation:
1. A:B = 2:3. B:C = 4:5. Equate B (LCM of 3,4 = 12) \(\to\) A:B:C = 8:12:15.
2. C:D = 6:7. Equate C (LCM of 15,6 = 30) \(\to\) (8:12:15)\(\times\)2 : (6:7)\(\times\)5 = 16:24:30:35.
3. Total parts = \( 16 + 24 + 30 + 35 = 105 \).
4. A's share = \( \frac{16}{105} \times 8400 = 16 \times 80 = 1280 \).
Step 4: Final Answer:
The share of A is Rs. 1280.