A and B entered into a partnership and invested their respective amounts in…
2021
A and B entered into a partnership and invested their respective amounts in the ratio of 2: 1. C and D entered into another partnership with initial investment ratio of 2: 1. Total investment of A and B was 25% less than that of C and D. If total profit of all 4 person at the end of year is Rs.10500, then find profit of A.
- A.
Rs.2000
- B.
Rs.1500
- C.
Rs.3000
- D.
Rs.4000
- E.
Rs.3600
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Show answer & explanation
Correct answer: C
Concept
When partners invest for the same period of time, the annual profit is divided among them in the same ratio as their invested capitals. So if we can express every partner's capital as a share of one common total, each person's profit is simply that share of the overall profit.
Application
Express both groups on a common base. A and B together invested 25% less than C and D, so (A+B) : (C+D) = 75 : 100 = 3 : 4.
Split each group by its internal ratio. Within the group of value 3, A : B = 2 : 1; within the group of value 4, C : D = 2 : 1. To split 4 in the ratio 2 : 1 with whole numbers, scale both groups by 3, giving (A+B) = 9 and (C+D) = 12.
Find each individual capital. A : B from 9 gives A = 6, B = 3. C : D from 12 gives C = 8, D = 4.
Combined capital ratio A : B : C : D = 6 : 3 : 8 : 4, total = 21 parts.
A's profit = (6 / 21) of total profit = (6 / 21) × 10500 = 3000.
Cross-check
Adding all four shares: A = (6/21)×10500 = 3000, B = (3/21)×10500 = 1500, C = (8/21)×10500 = 4000, D = (4/21)×10500 = 2000. Sum = 3000 + 1500 + 4000 + 2000 = 10500, which matches the given total profit, so A's profit is Rs.3000.