Question

Old ratio of two partners A and B is 5:3, they admit another partner C for 1/4th share. The new ratio among A, B and C is:

• A. 15 : 9 : 8
• B. 20 : 12 : 8
• C. 5 : 3 : 2
• D. 9 : 6 : 5

Hint:

When a new partner joins a partnership and is given a share, the original partners’ shares are reduced proportionally to accommodate the new partner’s share.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
The original ratio between A and B is 5:3, which means for every 8 parts, A gets 5 parts, and B gets 3 parts. Partner C is admitted for a 1/4th share. So, the total share is now 1 (for A and B) + 1/4 (for C).
Step 2: Calculating the total share.
The total share is 1 (A + B) + 1/4 (C), which is equivalent to 5/4. The original share of A and B must be adjusted for the new total. Thus, A's new share = \( \frac{5}{8} \times \frac{4}{5} = \frac{5}{4} \). Similarly, for B, we have: B's new share = \( \frac{3}{8} \times \frac{4}{5} = \frac{3}{4} \).
Step 3: Adjusting the shares.
Now, we have: A = \( 15 \), B = \( 9 \), and C = 8, which leads to the new ratio of 15 : 9 : 8.
Step 4: Conclusion.
The new ratio of shares among A, B, and C is 15:9:8. Final Answer:} 15 : 9 : 8.