A, B and C are partners in a firm in the ratio of 5 : 3 : 2. B retires from the firm. A and C want to have the same previous ratio. The new ratio of A and C will be

Solution (By Examveda Team)

First, imagine A, B, and C are partners in a business, and they share profits based on a rule called a ratio. Their original sharing rule is 5 : 3 : 2. This means for every 10 parts of profit (5 + 3 + 2 = 10), A gets 5 parts, B gets 3 parts, and C gets 2 parts.

Now, B decides to retire from the firm. This means B is no longer a partner, and B's share (3 parts) is no longer part of the firm's profit sharing among the remaining partners.

The important instruction is: "A and C want to have the same previous ratio." This sentence is key! It means that even though B is gone, A and C want their sharing relationship between themselves to remain exactly as it was before B left. They don't want their *relative proportions* to each other to change.

Let's look at A and C's original parts relative to each other: Before B left, A had 5 parts and C had 2 parts in their sharing rule.

Since A and C want to maintain this *exact same relationship* or proportion between themselves after B has left, their new ratio will simply be their old ratio *to each other*.

So, if A had 5 parts and C had 2 parts when B was there, and they want to keep that specific relationship, then their new ratio of A to C will be 5 : 2.

This is like saying, "If A always gets 5 cookies for every 2 cookies C gets, and a third friend leaves, A and C still want to keep that 5-to-2 cookie distribution between themselves."

Therefore, the correct answer is Option C: 5 : 2.