Three partners, R, S, and K, form a partnership business with capitals in the ratio of 3:5:8. After four months, R, S, and K added Rs. 3000, Rs. 4500, and Rs. 6000, respectively. After the next four months, R and K withdrew Rs. 2500 and Rs. 4000, respectively, and S added an additional Rs. 3000. Two new partners, M and N, enter the business. M invested capital Rs. 3000 more than what R invested for the first four months, and N invested the same amount as K invested for the last four months. If M and N share the profit after one year in the ratio of 15:28, then find the investment of S for the last four months.

 Let investment of R, S and K is Rs. 3a, Rs. 5a and Rs. 8a respectively.  ATQ — Investment ratio of R, S and K =  [3x × 4 + (3x + 3000) × 4 + (3x + 3000 – 2500)  × 4] : [5x × 4 + (5x + 4500) × 4 + (5x + 4500 + 3000) × 4] : [8x × 4 + (8x + 6000) × 4 + (8x + 6000 – 4000)  × 4]  = (36x + 14000) : (60x + 48000) : (96x + 32000)  Investment of M = Investment of R for first four months + 3000 = (3x + 3000) Investment of N = Investment of K for last four months = (8x + 6000 – 4000)  ATQ —    (3a + 3000) x 12/(8a + 2000) x 12 = 15/28 10a - 7a = 7000 – 25000  3a = 4500 a = Rs 1500  S invested for last four months  = (5a + 4500 + 3000) = (5 × 1500 + 4500 + 3000) = Rs.15000