Concept of “Partnership” [साझेदारी]-03

Question: Manoj got Rs.6000 as his share out of the total profit of Rs.9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs.20000 for 6 months, whereas Ramesh invested his amount for the whole year, the amount invested by Ramesh was:[मनोज ने 9000 रूपये के कुल लाभ में 6000 रु अपने हिस्से के प्राप्त किये, जिसे उसने तथा रमेश ने मिलकर एक वर्ष के अंत में प्राप्त किया था. मनोज ने 20000 रु 6 महीनों के लिए निवेश किया, जबकि रमेश ने अपनी रकम पूरे वर्ष के लिए निवेश किया. बताएं कि रमेश के द्वारा निवेश की गयी रकम कितनी थी? ]  [Ans. (a) Rs.5000]   

(a)  Rs.5000 (b) Rs.60000(c) Rs.10000 (d) Rs.40000 (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: Manoj got Rs.6000 as his share out of the total profit of Rs.9000, so the share of Ramesh is Rs. 9000-Rs. 6000 = Rs. 3000.  Ratio of profits of Manoj and Ramesh is

P₁:P₂ = 6000:3000 = 2:1

Manoj has invested his capital for 6 months, while Ramesh for 12 months.

So, T₁:T₂ = 6:12 = 1:2

The ratio of capitals of Manoj and Ramesh can be determined as:

C₁:C₂ = P₁/T₁:P₂/T₂ = 2/1: 1/2 = 4:1

  [Capital of Manoj] = 4 ≡ Rs. 20000 (given)

[Capital of Ramesh] = 1 ≡? = Rs. 5000 Ans.

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Second Method: Manoj has invested Rs.20000 for 6 months, so his capital for one month is Rs. 20000× 6.

Ramesh has invested Rs. “x” for 12 months, so his capital for one month is Rs. x×12

Now, the Manoj got Rs.6000 as his share out of the total profit of Rs.9000, so the share of Ramesh is Rs. 9000-Rs. 6000 = Rs. 3000.

So, (20000× 6)/(x×12) = 2/1

Or, x = Rs. 5000 Ans.

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