The investment of B is 60% more than that of A, and the ratio of investment of B to that of C is 4 : 5. The ratio of the time for which A, B and C invested is 3 : 2 : 1, respectively. If A’s profit share is Rs. 3000, find the difference between the profit shares of B and
C.

ATQ, B’s investment is 60% more than A’s investment. So, A : B = 100 : 160 = 5 : 8 Also, B : C = 4 : 5 To combine, match B: From A : B = 5 : 8 and B : C = 4 : 5 Let B = LCM of 8 and 4 = 8 So, A : B = 5 : 8 and for B : C = 4 : 5, if B = 8 ⇒ multiply by 2 ⇒ B : C = 8 : 10 Hence, A : B : C = 5 : 8 : 10 Time ratio of A, B and C = 3 : 2 : 1 Profit ratio = Investment × Time A : B : C = 5 × 3 : 8 × 2 : 10 × 1 A : B : C = 15 : 16 : 10 A’s profit share = Rs. 3000 15 parts = 3000 1 part = 3000/15 = 200 Difference between profit shares of B and C = 16 parts − 10 parts = 6 parts 6 parts = 6 × 200 = Rs. 1200