Dividing a premium for sacrificing future profit share: A and B initially share profit in the ratio of their capitals ₹ 20,000 : ₹ 35,000 (i.e., 4 : 7). C joins so that A, B, C will share profits equally. C pays a premium ₹ 2,20,000 to compensate A and B for their sacrifice. In what ratio should A and B divide this premium?

Introduction / Context:
When a new partner joins and the sharing ratio changes, existing partners sacrifice part of their future profit. Any premium paid for this sacrifice must be divided in the ratio of the sacrifice amounts. We compute each partner’s sacrifice as “old share − new share.”

Given Data / Assumptions:

• Old ratio A : B = 4 : 7 ⇒ A_old = 4/11, B_old = 7/11.
• New ratio with C = 1/3 each ⇒ A_new = B_new = 1/3.
• Premium = ₹ 2,20,000 split between A and B in the ratio of sacrifice.

Concept / Approach:
Sacrifice_A = A_old − A_new; Sacrifice_B = B_old − B_new. Divide the premium in Sacrifice_A : Sacrifice_B. Simplify the fraction ratio carefully.

Step-by-Step Solution:

Verification / Alternative check:
The larger sacrifice belongs to B (from 7/11 down to 1/3), which aligns with the 1 : 10 split favoring B’s compensation.

Why Other Options Are Wrong:
10 : 1 reverses the sacrifice; 9 : 10 and 10 : 9 do not match exact fractional differences; 4 : 7 is the old capital ratio, not the sacrifice ratio.

Common Pitfalls:
Using “new − old” instead of “old − new” for sacrifice or dividing the premium by old capital ratio instead of by the sacrifice ratio.

Final Answer:
1 : 10