Chapter 9: PARTNERSHIP THEORY
When A and B are partners and both invest in a ratio say
x:y but at the same time then their ratio of profits sharing
is same as their investment ratio i.e. x:y.
However if A invests 'x' amount for 'p' months and B
invests 'y' amount for 'q' months then their share in
A's share : B's share = x * p : y * q
Questions and Answers
Q. If A invests 1,20000 B invests 1,35000
and C invests 150000 then find their share in profits if
profit is 56700.
A. Ratio of their investments is 8:9:10
since we can divide by 15 after cancelling zeros. Then A's
share is 8/27 as 8/8+9+10 and similarly B's share is 9/27
and C's share is 10/27. Using these we can get their final
Q.Alfred started a business
investing Rs. 45,000. After 3 months, Peter joined him with
a capital of Rs. 60,000. After another 6 months, Ronald
joined them with a capital of Rs. 90,000. At the end of the
year, they made a profit of Rs. 16,500. Find the share of
A. Alfred's investment = 45000 * 12
months; Peter's investment = 60000 * 9 months; Ronald's
investment = 90000 * 6 months;
A:B:C = 45*12 : 60*9: 90*6 = 3*12:4*9:6*6 = 2:2:1 so
Alfred's share is 2/5, Peter's share is 2/5 and Ronald's is
1/5. Use this to get their shares.
Q. A, Band C start a business each
investing Rs. 20,000. After 5 months A withdrew
Rs.6000 B withdrew Rs. 4000 and C invests Rs. 6000
more. At the end of the year, a total profit of Rs. 69,900
was recorded. Find the share of each.
A. A's share = 20000*5 + 14000*7
B's share = 20000*5 + 16000 * 7 and C's share = 20000*5 +
A:B:C = 205:212:282
Q. A, Band C enter into partnership. A
invests 3 times as much as B and B invests two-third of what
C invests. At the end of the year, the profit earned is Rs.
6600. What is the share of B ?
A. Let C's share be 'x' and so B gets
2x/3 and then A gets 2x so their ratio is
A:B:C = 2: (2/3) : 1, multiplying by 3 throughout we get
A:B:C = 6:2:3
Q. A invested Rs. 76,000
in a business. After few months, B
joined him Rs. 57,000. At the end of the year, the
total profit was divided between them in ratio 2 : 1.
After bow many months did B join?
A. A's share = 76000*12 and B's share is
57000 * 'x'
A:B = 76*12 : 57 * x = 2:1 we get x=8 months.
So B invested for 8 months hence he joined after 4 months.
Q. A, B and C enter into a partnership by
investing in the ratio of 3 : 2 : 4. After 1 year,
B invests another Rs. 2,70,000
and C, at the end of
2 years, also invests Rs.2,70,000. At the
end of three years, profits are shared in the ratio of 3 : 4
: 5. Find initial investment of each.
A. The initial investment's of A,B,C be
3x, 2x and 4x.
A's share 3x * 36, B's share is 2x * 12 + 270000 * 24, C's
share is 4x * 24 + 270000 * 12.
A:B:C = 3:4:5 using this ratio we can get their shares.
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