P, Q & R are partners in a partnership firm named RAWAT SOLUTIONS and sharing profits in the ratio of 4:3:1. Q retires and sold his share of profits to other partners for ₹8,100. ₹3,600 was paid by P and ₹4,500 was paid by R. Profit for the year after Q's retirement is ₹10,500.

In which ratio ₹10,500 profit will be divided among partners?

2:1

The correct answer is option 4- 2:1

As Q is retired from the firm and the profit is after his retirement so it will be distributed in the new ratio means 2:1.

Old ratio is 4:3:1
As both partners gaining ratio is 4:5 means they acquire Q's share(3/8) in this ratio.
So, P acquires = 4/9 x 3/8
                       = 12/72 or 1/6

R acquires = 5/9 x 3/8
                 = 15/72 or 5/24

New share = Old share + Acquired share

P's new share = 4/8 + 1/6
                       = (12 +4)/24
                       = 16/24 or 2/3

R's new share = 1/8 + 5/24
                       = (3 +5)/24
                       = 8/24 or 1/3

New ratio = 2/3 : 1/3
                = 2:1