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Solved Examples(Set 3) - Partnership

 11. A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? A. 14200 B. 14700 C. 14800 D. 14500

Explanation:

Total amount invested = 50000

Assume that investment of C $=x$.
Then investment of B $=5000+x$,
Investment of A $=4000+5000+x=9000+x$

$x+5000+x+9000+x=50000\\ \Rightarrow 3x+14000=50000\\ \Rightarrow 3x=50000-14000=36000\\ \Rightarrow x=\dfrac{36000}{3}=12000$

Investment of C $=x=12000$
Investment of B $=5000+x=17000$
Investment of A $=9000+x=21000$

Ratio of the investment of A, B and C
$=21000:17000:12000\\=21:17:12$

Share of A = Total profit $×\dfrac{21}{50}$
$=35000×\dfrac{21}{50}=700×21=14700$

 12. A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? A. 60 B. 35 C. 55 D. 45

Explanation:

A : B : C
$=10×7:12×5:15×3\\=2×7:12×1:3×3\\=14:12:9$

Amount that C should pay
$=175×\dfrac{9}{35}=5×9=45$

 13. A and B entered into a partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew $\dfrac{1}{4}$ of his capital and B withdrew $\dfrac{1}{5}$ of his capital. At the end of 10 months, the gain was Rs.760. What is A's share in the profit? A. 310 B. 350 C. 330 D. 370

Explanation:

Ratio of the initial capital of A and B = 4 : 5

Hence we can take the initial capitals of A and B as $4x$ and $5x$ respectively

Ratio in which profit will be divided
$=(4x×3)+\dfrac{3}{4}×4x×7$ $:(5x×3)+\dfrac{4}{5}×5x×7$
$=(12+21):(15+28)\\=33:43$

A's share $=760×\dfrac{33}{76}=330$

 14. A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B's contribution in the capital is A. 9000 B. 8000 C. 10000 D. 7000

Explanation:

Ratio in which profit is divided $=2:3$

Assume that B's contribution to the capital $=b$

$3500×12:b×7 = 2:3\\~\\ \Rightarrow 3500×12×3=2×b×7\\~\\ \Rightarrow b=\dfrac{3500×12×3}{2×7}\\~\\=500×6×3=9000$

 15. A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments? A. 20 : 22 : 12 B. 12 : 24 : 28 C. 20 : 49 : 64 D. 10 : 12 : 14

Explanation:

Ratio in which A,B and C shared the profit $=5:7:8$

Assume that the ratio of their investments $=a:b:c$
$\Rightarrow 14a:8b:7c=5:7:8 \quad \cdots(A)$

From (A),
$14a:8b=5:7\\ \Rightarrow 14a×7=8b×5\\ \Rightarrow 7a×7=4b×5\\ \Rightarrow b=\dfrac{49a}{20}\quad \cdots(1)$

From (A),
$14a:7c=5:8\\ \Rightarrow 14a×8=7c×5\\ \Rightarrow 2a×8=c×5\\ \Rightarrow c=\dfrac{16a}{5}\quad \cdots(2)$

$a:b:c=a:\dfrac{49a}{20}:\dfrac{16a}{5}\\=1:\dfrac{49}{20}:\dfrac{16}{5}=20:49:64$