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?

1. 5 : 7 : 8
2. 20 : 49 : 64
3. 38 : 28 : 21
4. None of these

Answer:Option 1

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,

\begin{aligned} \frac{14 x}{8 y} = \frac{5}{7} \Rightarrow 98 x = 40 y \\ \Rightarrow y = \frac{49 x}{20} \\ And, \frac{14 x}{7 z} = \frac{5}{8} \\ \Rightarrow 112 x = 35 z \\ \Rightarrow z = \frac{112 x}{35} = \frac{16 x}{5} \\ So x : y : z = x : \frac{49 x}{20} : \frac{16 x}{5} \\ (Multiply by 20) \\ \Rightarrow 20 : 49 : 64 \end{aligned}

$\eqalign{ & \frac{{14x}}{{8y}} = \frac{5}{7} \Rightarrow 98x = 40y \cr & \Rightarrow y = \frac{{49x}}{{20}} \cr & {\text{And, }}\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \Rightarrow 112x = 35z \cr & \Rightarrow z = \frac{{112x}}{{35}} = \frac{{16x}}{5} \cr & {\text{So}}\,x:y:z = x:\frac{{49x}}{{20}}:\frac{{16x}}{5} \cr & ({\text{Multiply by 20}}) \cr & \Rightarrow 20:49:64 \cr}$

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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.

1. Rs. 4000
2. Rs. 5000
3. Rs. 6000
4. Rs. 7000

Answer:Option 1

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 \times \frac{4}{11}

$16500 \times \frac{4}{{11}}$ = 1500 × 4 = 6000.

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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 ?

1. Rs 2380
2. Rs 2300
3. Rs 2280
4. Rs 2260

Answer:Option 1

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{aligned} = (6970 \times \frac{14}{41}) \\ = Rs . 2380 \end{aligned}

$\eqalign{ & = \left( {6970 \times \frac{{14}}{{41}}} \right) \cr & = {\text{Rs}}{\text{. 2380}} \cr}$

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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

1. Rs. 600
2. Rs. 700
3. Rs. 800
4. Rs. 900

Answer:Option 1

Explanation:

Solution:

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

\begin{aligned} 4 p = 6 q = 10 r \\ \Rightarrow 2 p = 3 q = 5 r \\ \Rightarrow q = \frac{2 p}{3} \\ \Rightarrow r = \frac{2 p}{5} \\ P : Q : R = p : \frac{2 p}{3} : \frac{2 p}{5} \\ (Multiply by 15) \\ = 15 : 10 : 6 \\ R's share = 4650 \times \frac{6}{31} \\ = 150 \times 6 \\ = Rs . 900 \end{aligned}

$\eqalign{ & 4p = 6q = 10r \cr & \Rightarrow 2p = 3q = 5r \cr & \Rightarrow q = \frac{{2p}}{3} \cr & \Rightarrow r = \frac{{2p}}{5} \cr & {\text{P}}:{\text{Q}}:{\text{R}} = p:\frac{{2p}}{3}:\frac{{2p}}{5} \cr & ({\text{Multiply by 15}}) \cr & = 15:10:6 \cr & {\text{R's share}} = 4650 \times \frac{6}{{31}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 150 \times 6 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}900 \cr}$

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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?

1. Rs. 45
2. Rs. 50
3. Rs. 55
4. Rs. 60

Answer:Option 1

Explanation:

Solution:

\begin{aligned} A : B : C \\ = (10 \times 7) : (12 \times 5) : (15 \times 3) \\ = 70 : 60 : 45 \\ = 14 : 12 : 9 \\ C's rent = Rs . (175 \times \frac{9}{35}) \\ = Rs . 45 \end{aligned}

$\eqalign{ & A:B:C \cr & = \left( {10 \times 7} \right):\left( {12 \times 5} \right):\left( {15 \times 3} \right) \cr & = 70:60:45 \cr & = 14:12:9 \cr & {\text{C's rent}} = {\text{Rs}}{\text{.}}\left( {175 \times \frac{9}{{35}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}45 \cr}$

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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?

1. Rs. 48000
2. Rs. 48200
3. Rs. 48400
4. Rs. 48600

Answer:Option 1

Explanation:

Solution:

Assume that investment of C = x
Then, investment of A = 2x
Investment of B =

\frac{2 A}{3}

$\frac{{2{\text{A}}}}{3}$ =

\frac{4 x}{3}

$\frac{{4{\text{x}}}}{3}$ (since ratio of investment of A : B = 2 : 3 i.e B =

\frac{2 A}{3}

$\frac{{2{\text{A}}}}{3}$ )
A : B : C = 2x :

\frac{4 x}{3}

$\frac{{4{\text{x}}}}{3}$ : x = 2 :

\frac{4}{3}

$\frac{4}{3}$ : 1 = 6 : 4 : 3

\begin{aligned} B's Share \\ = 157300 \times \frac{4}{6 + 4 + 3} \\ = 157300 \times \frac{4}{13} \\ = 12100 \times 4 \\ = Rs . 48400 \end{aligned}

$\eqalign{ & {\text{B's Share}} \cr & = 157300 \times \frac{4}{{6 + 4 + 3}} \cr & = 157300 \times \frac{4}{{13}} \cr & = 12100 \times 4 \cr & = {\text{Rs}}{\text{. 48400}} \cr}$

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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?

1. Rs. 7500
2. Rs. 9000
3. Rs. 9500
4. Rs. 10,000

Answer:Option 1

Explanation:

Solution:

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

\begin{aligned} So B's Share \\ = Rs . 25000 \times \frac{3}{10} \\ = Rs . 7500 \end{aligned}

$\eqalign{ & {\text{So B's Share}} \cr & = {\text{Rs}}{\text{. }}25000 \times \frac{3}{{10}} \cr & = {\text{Rs}}{\text{. 7500}} \cr}$

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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

1. Rs. 8400
2. Rs. 11,900
3. Rs. 13,600
4. Rs. 14,700

Answer:Option 1

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{aligned} So A's Share \\ = Rs . 3 5000 \times \frac{21}{50} \\ = Rs . 14700 \end{aligned}

$\eqalign{ & {\text{So A's Share}} \cr & = {\text{Rs}}{\text{. 3}}5000 \times \frac{{21}}{{50}} \cr & = {\text{Rs}}{\text{. 14700}} \cr}$

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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:

1. Rs. 1425
2. Rs. 1500
3. Rs. 1537.50
4. Rs. 1576

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Let the total profit be Rs . 100 \\ After paying to charity, A's share \\ = R s . (95 \times \frac{3}{5}) = R s . 57 \\ If A's share is R s . 57, \\ Total profit = R s . 100 \\ If A's share R s . 855, \\ Total profit \\ = (\frac{100}{57} \times 855) = 1500 \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{total}}\,{\text{profit}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{100}} \cr & {\text{After}}\,{\text{paying}}\,{\text{to}}\,{\text{charity,}}\,{\text{A's}}\,{\text{share}} \cr & = Rs.\,\left( {95 \times \frac{3}{5}} \right) = Rs.\,57 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,{\text{is}}\,Rs.\,57, \cr & {\text{Total}}\,{\text{profit}} = Rs.\,100 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,Rs.\,855, \cr & {\text{Total}}\,{\text{profit}} \cr & = \left( {\frac{{100}}{{57}} \times 855} \right) = 1500 \cr}$

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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.

1. Rs. 1900
2. Rs. 2660
3. Rs. 2800
4. Rs. 2840

Answer:Option 1

Explanation:

Solution:

For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10