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# Solved Examples(Set 6) - Partnership

 26. In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? A. 48400 B. 48000 C. 48200 D. 48600

Explanation:

Assume that investment of C $=x$
Then, investment of A $=2x$
Investment of B $=\dfrac{4x}{3}$

A:B:C $=2x:\dfrac{4x}{3}:x$
$=2:\dfrac{4}{3}:1=6:4:3$

B's share $=157300×\dfrac{4}{6+4+3}$
$=157300×\dfrac{4}{13}=12100×4=48400$

 27. P, Q and R started a business by investing Rs.120000, Rs.135000 and Rs.150000 respectively. Find the share of each, out of the annual profit of Rs.56700. A. 17850, 18500, 22000 B. 17850, 18900, 21000 C. 16800, 18900, 21000 D. 16800, 18900, 22000

Explanation:

P : Q : R = $120000:135000:150000$
$=120:135:150\\=24:27:30\\=8:9:10$

Share of P
$=56700×\dfrac{8}{27}=2100×8=16800$

Share of Q
$=56700×\dfrac{9}{27}=2100×9= 18900$

Share of R
$=56700×\dfrac{10}{27}=2100×10=21000$

 28. If 4 (P's Capital) = 6(Q's Capital) = 10(R's Capital), then out of the total profit of Rs 4650, R will receive A. 700 B. 800 C. 600 D. 900

Explanation:

Let P's capital be $p$,
Q's capital be $q$,
and R's capital be $r$

Then
$4p=6q=10r\\2p=3q=5r \cdots(A)$

From (A),
$q=\dfrac{2p}{3}~~\cdots(1)\\r=\dfrac{2p}{5}~~\cdots(2)$

$p:q:r=p:\dfrac{2p}{3}:\dfrac{2p}{5}$
$=15:10:6$

R's share $=4650×\dfrac{6}{31}=150×6=900$

 29. P, Q, R enter into a partnership. P initially invests 25 lakh and adds another 10 lakh after one year. Q initially invests 35 lakh and withdraws 10 lakh after 2 years. R's investment is Rs 30 lakh. In what ratio should the profit be divided at the end of 3 years? A. 18:18:19 B. 18:19:19 C. 18:19:18 D. 19:19:18

Explanation:

P : Q : R
$=(25×1+35×2):(35×2+25×1)$ $:(30×3)$
$=95:95:90\\=19:19:18$

 30. P, Q, R enter into a partnership and their share are in the ratio $\dfrac{1}{2}:\dfrac{1}{3}:\dfrac{1}{4}$. After two months, P withdraws half of his capital and after 10 more months, a profit of Rs 378 is divided among them. What is Q's share? A. 120 B. 144 C. 114 D. 134

Explanation:

The ratio of their initial investment
$=\dfrac{1}{2}:\dfrac{1}{3}:\dfrac{1}{4}\\=6:4:3$

Let the initial investment of P, Q and R be $6x, 4x$ and $3x$ respectively.

A:B:C
$=(6x×2+3x×10):4x×12:3x×12$
$=(12+30):4×12:3×12\\=(4+10):4×4:12\\=14:16:12\\=7:8:6$

B's share $=378×\dfrac{8}{21}=18×8=144$