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# Solved Examples(Set 2) - Partnership

 6. A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? A. 6 months B. 5 months C. 8 months D. 7 months

Explanation:

Let B joined for $x$ months. Then

$85000×12:42500×x=3:1\\ \Rightarrow 850×12:425x=3:1\\ \Rightarrow 850×12×1=3×425x\\ \Rightarrow 850×4=425x\\ \Rightarrow x=8$

 7. A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join? A. 5 months B. 6 months C. 7 months D. 4 months

Explanation:

Assume that C was there in the business for $x$ months

A:B:C
$=40000×12:60000×10:120000×x\\=40×12:60×10:120x\\=40:5×10:10x\\=8:10:2x\\=4:5:x$

C's share $=375000×\dfrac{x}{9+x}=\dfrac{375000x}{9+x}$

$\Rightarrow \dfrac{375000x}{9+x}=150000\\ \Rightarrow \dfrac{375x}{9+x}=150\\ \Rightarrow 15x=6(9+x)\\ \Rightarrow 5x=18+2x\\ \Rightarrow 3x=18\\ \Rightarrow x=6$

It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined.

 8. A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? A. 1600 B. 1400 C. 1200 D. 1500

Explanation:

Assume that the total profit is $x$

Since 5% goes for charity, 95% of $x$ will be divided between A and B in the ratio $3:2$
Therefore, A's profit $=\dfrac{95x}{100}×\dfrac{3}{5}$

Given that A's share is Rs. 855. Therefore,
$\dfrac{95x}{100}×\dfrac{3}{5}=855\\ \Rightarrow \dfrac{95x}{100}=855×\dfrac{5}{3}=285×5=1425\\~\\ \Rightarrow x=\dfrac{1425×100}{95}\\=\dfrac{285×100}{19}=1500$

Hence the total profit = 1500

 9. A, B and C invest in a partnership in the ratio: $\dfrac{7}{2},\dfrac{4}{3},\dfrac{6}{5}$. After 4 months, A increases his share 50%. If the total profit at the end of one year is Rs.21,600, then what is B's share in the profit? A. Rs. 3000 B. Rs. 5000 C. Rs. 2000 D. Rs. 4000

Explanation:

Ratio of the initial investment
$=\dfrac{7}{2}:\dfrac{4}{3}:\dfrac{6}{5}=105:40:36$

Therefore, let the initial investments of A, B and C be $105x, 40x$ and $36x$ respectively

A increases his share 50% after 4 months. Hence the ratio of their investments
$=(105x×4)+\left(105x×\dfrac{150}{100}×8\right)$ $:40x×12:36x×12$
$=105+\left(105×\dfrac{3}{2}×2\right)$ $:40×3:36×3$
$=105×4:40×3:36×3\\=35×4:40:36\\=35:10:9$

B's share = total profit × $\dfrac{10}{54}$
$=21600×\dfrac{10}{54}=4000$

 10. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. A. 1000 B. 2660 C. 4000 D. 2300

Explanation:

A is a working member and for that, he receives 5% of the profit
= 5% of 7400 $=\dfrac{5×7400}{100}=370$

Remaining amount $=7400-370=7030$

Ratio of their investments
$=6500×6:8400×5:10000×3\\=65×6:84×5:100×3\\=13×6:84:20×3\\=13×2:28:20\\=13:14:10$

Share of B in the profit
$=7030×\dfrac{14}{37}=190×14=2660$