"Concept of Partnership”-05

Question: A puts Rs.600 more in a business than B, but B has invested his capital for 5 months while A has invested his for 4 months. If the share of A is Rs.48 more than that of B out of the total profits of Rs.528, find the capital contributed by A? [Ans. (d) Rs.1800]                                                                                            

(a) Rs.2000 (b) Rs.2500 (c) Rs.1500 (d) Rs.1800 (e) None of these

Solution:

Detailed Explanation:

Concept: “Profits are always distributed in the ratio of the capitals, if other conditions are the same” – This is the base line of the chapter “PARTNERSHIP.” If the timing are not the same, the profits are distributed in the ratio of the products of corresponding “capital” and “time period”.

                “Capital” and “time period” are inversely proportional. Capitals are in the ratios of profits divided by corresponding timing. Similarly, Time periods are in the ratios of profits divided by the corresponding capitals. The facts can be summarized as:

(1)     P₁:P₂: P₃ = C₁× T₁: C₂×T₂: C₃× T₃

(2)     C₁:C₂:C₃ = P₁/T₁:P₂/T₂: P₃/T₃

(3)     T₁:T₂:T₃ = P₁/C₁:P₂/C₂: P₃/C₃

Let the profit of A is x and profit of B is y. Given that x+y = 528 and x-y = 48

Solving them, we get x = Rs.288 and Rs.240

The ratio of profits = 288: 240 = 6: 5

Their time periods are 4 months and 5 months respectively

So, their ratio = 4: 5 

Ratio of capitals = 6/4: 5/5 = 3: 2

A’s capital = 3 ≡

B’s capital = 2 ≡

Sum of capitals = 5 ≡

Difference between capital = 1 ≡ Rs. 600 (given)

A’s capital = 3 ≡? = Rs.1800 Ans.