Question
P, Q, and R enter a partnership by investing their
capital in the ratio of 2/5 :3/4: 5/8. After 4 months, P increased his capital by 50%, but Q decreased his capital by 20%. What is the share of Q in the total profit of 28,210 at the end of a year?Solution
Ratio of capitals invested by A, B and C = (2/5) /:3/ 4: 5: 8 = 16:30: 25 Let capital of A, B, and C are 16x, 30x, and 25x respectively. Capital of A at the end of the year = 16x × 4 + 24x × 8 = 64x + 192x = 256x Capital of B at the end of the year = 30x × 4 + 24x × 8 = 120x + 192x = 312x Capital of C at the end of the year = 25x × 12 = 300x Capital ratio of A, B, and C at the end of the year = 256x :312x :300x = 64x: 78x :75x According to the question- 64x+78x+75x =28210 217x =28210 x=130 Share of Q =78x =78×130 =10,140.
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