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# Solved Examples(Set 4) - Partnership

 16. A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in --- proportion. A. 6 : 10 : 5 B. 5 : 3 : 4 C. 3 : 4: 5 D. 10 : 5 : 4

Explanation:

Initial investment capital ratio of A and B = 3 : 5

Let initial capital of A and B be $3x$ and $5x$ respectively.

Amount that C invested after 6 months $=5x$ (since it is equal to B's investment)

Ratio in which profit should be distributed after 1 year
$=3x×12:5x×12:5x×6\\=3×12:5×12:5×6\\=3×2:5×2:5\\=6:10:5$

 17. A and B partner in a business. A contribute $\dfrac{1}{4}$ of the capital for 15 months and B received $\dfrac{2}{3}$ of the profit. For how long B's money was used? A. 12 months B. 16 months C. 14 months D. 10 months

Explanation:

B received $\dfrac{2}{3}$ of the profit.
Then A received remaining $\dfrac{1}{3}$ of the profit.
=> A : B $=\dfrac{1}{3}:\dfrac{2}{3}=1:2$

Let the total capital $=x$
Then A's capital $=\dfrac{x}{4}$
B's capital $=x-\dfrac{x}{4}=\dfrac{3x}{4}$

Assume B's money was used for $b$ months
Then A:B $=\dfrac{x}{4}×15:\dfrac{3x}{4}×b$

$\Rightarrow \dfrac{15x}{4}:\dfrac{3bx}{4}=1:2\\ \Rightarrow 15:3b=1:2\\ \Rightarrow 5:b=1:2\\ \Rightarrow 5×2=1×b\\ \Rightarrow b=10$

 18. A, B and C started a partnership business by investing Rs.27000, Rs.72000, Rs.81000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit? A. 90000 B. 80000 C. 70000 D. 120000

Explanation:

A:B:C $=27000:72000:81000$
$=3:8:9$

Let total profit $=p$

Then $p×\dfrac{9}{20}=36000$

$p=\dfrac{36000×20}{9}=80000$

 19. A and B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit, what is their total profit? A. 34000 B. 30000 C. 28000 D. 32000

Explanation:

Suppose B's investment $=x$.
Then A's investment $=3x$

Suppose B's period of investment $=y$
then A's period of investment $=2y$

A : B $=3x×2y:xy=6:1$

Total profit $×\dfrac{1}{7}=4000$
=> Total profit $=4000×7=28000$

 20. P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is A. 60000 B. 70000 C. 40000 D. 50000

$40000:q=2:3\\ \Rightarrow 40000×3=2q\\ \Rightarrow q=\dfrac{40000×3}{2}=60000$