Concept of “Partnership"-04

Question: A began a business with Rs.450 and was joined afterwards by B with Rs.300. When did B join if the profits at the end of the year were divided in the ratio 2: 1. [Ans. (b) 3 months] 

(a)  9 months (b) 3 months (c) 4 months (d) 6 months (e) none of these

Solution:

Detailed Explanation:

Concept: “Profits are always distributed in the ratio of the capitals, 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 “timing”.

                “Capital” and “timing” are inversely proportional. Capitals are in the ratios of profits divided by corresponding timing. Similarly, Timing 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

First Method: In the given question, capitals are respectively Rs 450 and 300; while the ratio of their timing is 12 months and x months. X is to be determined.

(450 × 12)/(300 × x) = 2/1

Or, x = 9 months

12 – 9 = 3 months Ans.

Second Method: T₁:T₂: = P₁/C₁:P₂/C₂ = 2/450:1/300 = 4: 3

4 ≡ 12 months

3 ≡? = 9 months

12 – 9 = 3 months Ans.