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1.	In a partnership business the ratio of the capitals of three friends is `3:4:5`. In the next year, if their capitals be increased by 10% , 15% and 20% respectively, then at theend of the second year at what ratio should their profits be distributed?
Answer» Let the capitals of three friends be Rs. `3x, Rs. 4x` and `Rs. 5x` `(3x+3x xx10/100):(4x+4x xx 15/100):(5x+5x xx 20/100)` `=(33x)/10:(23x)/5:6x=33:46:60` Hence the required of the profit `=33:46:60`

2.	Fill in the blanks: (i) Partnership busines is of ______________type. (ii) Whithout any other conditions in partnership business if the capitals of all partners are invested for the same time, then such a business is called_____________. (iii) Without any other conditions in partnership business, if the capitals of all the partners are invested for different time period , then such a business is called________________.
Answer» two, simple, mixed

3.	The ratio of capitals of three persons is `3:8:5` and the profit of 1st person is Rs. 60 less of the 3rd person, calculate the total profit in this business.
Answer» The ratio of the capitals of three person is `3:8:5` `:.` The ratio of their profit is `3:8:5` Let the profit of 1st and 3rd person be Rs. `3x` and Rs. `5x` As per question `5x-3x=60` `implies2x=60impliesx=30` `:.` Profit of the first friend `=Rs. 3x=Rs. 3xx30=Rs. 90` Profit of the second friend `=Rs. 8x =Rs. 8xx30=Rs. 240` Profit of the third `=Rs. 5x=Rs. 5xx30=Rs. 150` Hence, the total profit `=Rs. (90+240+150)=Rs. 480`

4.	At the beginning of a year A, B and C jointly started a business. A invested `1/3` part of the capital and B invested an amount eqwual to the total capital of A and C. If the profit be Rs. 840 at the end of the year, then find the profits of each of them.
Answer» Let the capital be Rs. `x` So A invested `Rs. x/3` and the investement of B and C is `Rs.(x-x/3)=Rs. (2x)/3`………..1 As per question the investment of `B=Rs. x/3+` investment of C `implies` (Capital of B)`-` (Capital of C)`=Rs. x/3`…….2 Now adding 1 and 2 we get `2xx("Capital of B")=((2x)/3)+x/3)=Rs. x` `:.` Capital of `B=Rs. x/2` `:.` From 1 we get capital of `C=Rs. ((2x)/3-x/2)=Rs. x/6` So (Capital of A: (capital of B): (capital of C)`=x/3:x/2:x/6=1/3:1/2:1/6=2:3:1` `:.` The part of the capital of `A=2/(2+3+1)=2/6` The part of the capital of `B=3/6` and the part of the capital of `C=1/6` So from Rs. 840 A will get `Rs. 840xx2/6=Rs. 280` B will get RKs. `840xx3/6=Rs. 420` and C will get Rs. `840xx1/6=Rs. 140` Hence the profits of A,B and C are Rs. 280, Rs. 420 and Rs. 140 respectively.

5.	In the year 2015, A invested Rs. 800 on 1st January, B invested Rs. 600 on 1st May and C invested Rs. 500 on 1st July. If the total profit of that year be Rs. 3480, find the profit of each of them.
Answer» Here the capital of a was invested for 12 months, the capital of B was invested for 8 months and the capital of C was invested for 6 months. `:.` The ratio of (the capital of A): (the capital of B): (the capital of C) `=800xx12:600xx8:500xx6` `=16:8:5` So from Rs. 3480, A will get profit Rs. `3480xx16/(16+8+5)` `=Rs. 3480xx16/29=Rs. 1920` From Rs. 3480, B will get profit Rs. `3480xx8/29=Rs. 960` From Rs. 3480, C will get profit Rs. `3480xx5/29=Rs. 600` Hence the profit of A,B and C will be Rs. 1920, Rs. 960 and Rs. 600 respectively.

6.	Amal and Bimal started a business. Amal invested Rs. 500 for 9 months and Bimal invested some money for 6 months. If they make a profit of Rs. 69 in a year and Bimal gets profit share of Rs. 46, the capital of Bimal in the business isA. Rs. 1500B. Rs. 3000C. Rs. 4500D. Rs. 6000
Answer» Total profit Rs. 69. Profit of Bimal is Rs. 46. `:.` Profit of Ajmal `=Rs ( 69-46)=Rs. 23` `:.` Profit of Ajmal: Profit of Bimal `=23:46=1:2` `:.` Capital of Ajmal : Capital of Bimal `=1:2` `:.` Capital of Amal with respect of 1 month `=Rs. 500xx9=Rs. 4500` `:.` Capital of Bimal with respect of 1 month `=Rs. 4500xx3/1xx2/(1+2)=Rs. 9000` Since Bimal invested his capital for 6 months. `:.` Capital of Bimal `=Rs. (9000+6)=Rs. 1500` `:.` a is correct.

7.	In a business, A invested 2 times capital than B and for a period of time which is also 3 times than . If B gets Rs. 12000 from the profit, then what is the total profit?
Answer» Let B invested Rs. `x` and `y` years. So the capital of `A=Rs. 2x` and time `=3y` years. `:.`The ratio of their profit is `(2x xx 3y):xy` `=(6xy)/(xy)=6/1` Let the total profit `=Rs. P` `:.` The profit of `B=Rs. Pxx1/(6+1)=Rs. P/7` As per question `P/7=10000impliesP=84000` Hence the required total profit `=Rs. 84000`

8.	Two friends invested Rs. 40000 and Rs. 50000 respectively to start a business. They made a contract that they would divide 50% of the profit equally between themselves and the remining profit in the Ratio of the their capitals. Calculate the share of profit of the first friend if it is Rs. 800 less than that of the second friend.
Answer» The ratio of capitals of the two two friends `=40000:50000=4:5` So the part of the capital of the first friend `=4/(4+5)=4/9` and the part of the capital of the second friend `=5/9` Let the profit be Rs. `x` So Rs. `x/2` is distributed equally between the two friends. So each friend gets `Rs. (x/2)/2=Rs. x/4` Again Rs. `(x-x/2)=Rs. x/2` is distributed according to the ratio of their capitals. `:.` From this Rs. `x/2` the first friend will get `Rs. x/2xx5/9=Rs. (5x)/18` As per question `((5x)/14+x/4)-((4x)/14+x/4)=800` or `(5x)/17-(4x)/18=800` or `(5x-4x)/14=800` or `x=800xx18` or `x=14400` `:.` The total profit `=Rs. 14400` So the first friend will get profit `Rs. ((4x)/18+x/4)` `=Rs. ((4xx14400)/18+14400/4)=Rs. (3200+3600)=Rs. 6800` Hence the profit of the first friend will be Rs. 6800.