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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?

A. 5 : 7 : 8

B. 20 : 49 : 64

C. 38 : 28 : 21

D. None of these

Discuss

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}

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.

A. Rs. 4000

B. Rs. 5000

C. Rs. 6000

D. Rs. 7000

Discuss

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}

= 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 ?

A. Rs. 2380

B. Rs. 2300

C. Rs. 2280

D. Rs. 2260

Discuss

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}

4. P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is

A. Rs. 40000

B. Rs. 50000

C. Rs. 60000

D. Rs. 70000

Discuss

Solution:

Let the amount invested by Q = q.

\begin{aligned} 40000 : q = 2 : 3 \\ \Rightarrow \frac{40000}{q} = \frac{2}{3} \\ \Rightarrow q = 40000 \times \frac{3}{2} \\ = Rs . 60000 \end{aligned}

5. 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. Rs. 600

B. Rs. 700

C. Rs. 800

D. Rs. 900

Discuss

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}

6. 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?

A. Rs. 40

B. Rs. 30

C. Rs. 45

D. Rs. 50

Discuss

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}

7. 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. Rs. 48000

B. Rs. 48200

C. Rs. 48400

D. Rs. 48600

Discuss

Solution:

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

\frac{2 A}{3}

\frac{4 x}{3}

(since ratio of investment of A : B = 2 : 3 i.e B =

\frac{2 A}{3}

)
A : B : C
= 2x :

\frac{4 x}{3}

: x
= 2 :

\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}

8. 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?

A. Rs. 7500

B. Rs. 9000

C. Rs. 9500

D. Rs. 10,000

Discuss

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}

9. P, Q, R enter into a partnership. P initially invests 25 lakh & adds another 10 lakhs after one year. Q initially invests 35 lakh & withdrawal 10 lakh after 2 years and R invests Rs 30 Lakhs . In what ratio should the profit be divided at the end of 3 years?

A. 18 : 19 : 19

B. 18 : 18 : 19

C. 19 : 19 : 18

D. 18 : 19 : 19

Discuss

Solution:

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

10. 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

A. Rs. 8400

B. Rs. 11,900

C. Rs. 13,600

D. Rs. 14,700

Discuss

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}

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