Partnership
1.Three partners 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?

Explanation:

Solution:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,

2.Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.

Explanation:

Solution:
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A : B : C =6x : 4x : x
= 6 : 4 : 1
B's share =
$16500×\frac{4}{11}$
= 1500 × 4 = 6000.

3.Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?

Explanation:

Solution:
Now as per question, Kamal invested for 12 months and Sameer invested for 7 months.
So Kamal : Sameer = (9000 × 12) : (8000 × 7)
= 108 : 56
= 27 : 14
Sameer Ratio in profit will be
$\begin{array}{rl}& =\left(6970×\frac{14}{41}\right)\\ & =\text{Rs}\text{. 2380}\end{array}$

4.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

Explanation:

Solution:
Let
P's capital = p,
Q's capital = q and
R's capital = r.
Then

5.A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?

Explanation:

Solution:

6.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?

Explanation:

Solution:
Assume that investment of C = x
Then, investment of A = 2x
Investment of B =
$\frac{2\text{A}}{3}$
=
$\frac{4\text{x}}{3}$
(since ratio of investment of A : B = 2 : 3 i.e B =
$\frac{2\text{A}}{3}$
)
A : B : C = 2x :
$\frac{4\text{x}}{3}$
: x = 2 :
$\frac{4}{3}$
: 1 = 6 : 4 : 3
$\begin{array}{rl}& \text{B's Share}\\ & =157300×\frac{4}{6+4+3}\\ & =157300×\frac{4}{13}\\ & =12100×4\\ & =\text{Rs}\text{. 48400}\end{array}$

7.A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

Explanation:

Solution:
A : B : C
= (20,000 × 24) : (15,000 × 24) : (20,000 × 18)
= 4 : 3 : 3.

8.A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives

Explanation:

Solution:
Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000
So, x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
$\begin{array}{rl}& \text{So A's Share}\\ & =\text{Rs}\text{. 3}5000×\frac{21}{50}\\ & =\text{Rs}\text{. 14700}\end{array}$

9.A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{total}\phantom{\rule{thinmathspace}{0ex}}\text{profit}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{100}\\ & \text{After}\phantom{\rule{thinmathspace}{0ex}}\text{paying}\phantom{\rule{thinmathspace}{0ex}}\text{to}\phantom{\rule{thinmathspace}{0ex}}\text{charity,}\phantom{\rule{thinmathspace}{0ex}}\text{A's}\phantom{\rule{thinmathspace}{0ex}}\text{share}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(95×\frac{3}{5}\right)=Rs.\phantom{\rule{thinmathspace}{0ex}}57\\ & \text{If}\phantom{\rule{thinmathspace}{0ex}}\text{A's}\phantom{\rule{thinmathspace}{0ex}}\text{share}\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}57,\\ & \text{Total}\phantom{\rule{thinmathspace}{0ex}}\text{profit}=Rs.\phantom{\rule{thinmathspace}{0ex}}100\\ & \text{If}\phantom{\rule{thinmathspace}{0ex}}\text{A's}\phantom{\rule{thinmathspace}{0ex}}\text{share}\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}855,\\ & \text{Total}\phantom{\rule{thinmathspace}{0ex}}\text{profit}\\ & =\left(\frac{100}{57}×855\right)=1500\end{array}$

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. Calculate the share of B in the profit.