Ratio of Division of Gains
• The amount investment of all the partners are for the same time period, the gain or loss amount is distributed among the partners in the ratio of their investments amounts.
Formula:- Capital x Time= Profit
Suppose, Prashant and Anil invest some money Rs. M1 and M2 respectively for a year in a business, at the end of year profit will be distributed among them
( Prashant share of profit ) : ( Anil share of profit ) = M1 x 12 : M2 x 12 = M1 : M2 = Prashant : Anil
• When investments are for different time periods, then equivalent capital are calculated a unit of time by taking (Capital x number of unit of time).
(Time should be measured in terms of year)
If someone join after 3 months, then total time should be counted as (12-3= 9 months)
Suppose, Prashant invests Rs. 7000 for 1 year and Anil invests Rs. 6000 for 9 months then
( Prashant share of profit ) : ( Anil share of profit ) = 7000 x 12 : 6000 x 9 = 84000:54000 =84:54
Here are some solved examples
Example 1: Rahim invest money into a new business Rs. 7000/- After eight months Ram joined him with Rs 9000. What should be profit they earn and distributed at the end of the year 2
Answer : 7000 x 12:9000 x 4 = 84000:36000 = 7:3
Example 2: A and B started a business with partnership. A joined Rs.6000. How much amount would B invest so that profit after one year be divided in the ratio of 2 : 3
Answer - 6000 x 12 / B x 12 = 2 / 3
B = 9000
Example 3: Sushant started a business and he invest in it Rs 45,000 After 4 month Raju joined him with capital of Rs 75,000. End of the year they gained profit was Rs 47500, Find the Sushant share of profit.
Answer : Share of profit ratio = Sushant:Raju = 45,000 x 12:75000 x 8 = 54,0000:60,0000 = 9:10
Share of profit of Sushant is 47500 x 9 / 19 = 22500.
Example 4: Sameer and Prashant started a business in partnership. Sameer invested Rs.6000 in it. After 1 year what amount Prashant should invest that there profit margin would be in the ratio of 3:5?
Answer : 6000 x 12 / P x 12 = 3 / 5
P= 10,000
Example 5: Prachi, Puja, Poulomi Started business of Rs 50,000. Prachi initial invested Rs 4000 more than Puja and Puja invested Rs 5000 more than Poulomi. Out of a total profit is Rs. 35,000, Find the Profit of Puja.
Answer : Let Poulomi = X then
Puja = X + 5000 and
Prachi = X + 5000 + 4000 = X + 9000
So, Prachi+ Puja+ Poulomi = (X + X + 5000) + (X + 9000) = 50,000
3X + 14,000 = 50,000
3X = 36,000 X = 12,000= Poulomi
Puja= 12000+5000= 17000
Prachi= 12000+9000= 21000
Prachi: Puja: Poulomi = 21000: 17000:12000 = 21 : 17 : 12
So, Puja's profit is = 35,000 x 17 / 50 = 11,900.
Example 6: Anil, Mukesh and Ritesh started a business by investing Rs. 125000 Rs 150000 and Rs 175000 respectively. Find the share of each, out of an annual profit of Rs. 93,600.
Answer : Ration of share = Ratio of their investment
Anil : Mukesh : Ritesh = 125000 : 150000 : 175000 = 5 : 6 : 7
Anil share = Rs. [93600 x 5 / 18 ] = 26000.
Mukesh share = Rs. [93600 x 6 / 18 ] = 31200.
Ritesh share = Rs. [93600 x 7 / 18 ] = 36400.
Example 7: Sushant started a software business by investing Rs. 40,000. After six months, Prashant Joined him with a capital of Rs. 60,000. After 3 years, they earned a profit of Rs . 27,900. What was Sushant's share in the profit
Answer :
Sushant:Prashant share= ( 40,000 x 36 ):( 60,000 x 30 ) = 1440000:1800000 = 4 : 5
Sushant:Prashant share= ( 40,000 x 36 ):( 60,000 x 30 ) = 1440000:1800000 = 4 : 5
Sushant's share is = Rs 27900 x 4 / 9 = Rs 12400.
Example 8: Jon and Harry started a partnership business investing some amount of money in the ratio of 2 : 3.Ryan joined them after six months with an amount equal to that of Harry. In what proportion should the profit at the end of one year be distributed among Jon Harry and Ryan
Answer - Let the initial investment money ratio of Jon and Harry is 2x and 3x So Jon , Harry and Ryan ratio of investment is
Answer - Let the initial investment money ratio of Jon and Harry is 2x and 3x So Jon , Harry and Ryan ratio of investment is
( Jon:Harry: Ryan ) = (2x X 12 ) : ( 3x X 12 ) ( 3x X 6 ) = 24:36:18 = 4 : 6 : 3
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