# Partnership Quiz 6

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# Partnership Quiz 6

### Introduction

Partnership Quiz 6 chapter deals with profit and loss related problems. Profit and/or loss is shared among the partners based on the sum of money invested by individual partners and the time period of the investment.
For example: A partner who has invested the highest amount of money/resources will receive the highest share of the profit at the end of the year provided all the partners have invested for the same time period.
Ratio of Division of Gains:
1. Suppose A and B invest Rs. $x$ and Rs. $y$ respectively for a year in a business, then at the end of the year:
(A's share of profit) : (B's share of profit) = $x$ : $y$
Here investment of all partners are for same time, and the gain or loss is distributed among them in the ratios of their investments.
2. Suppose A invests Rs. $x$ for 'p' months and B invests Rs. $y$ for 'q' months, then
(A's share of profit) : (B's share of profit) = $x$p : $x$q
Here investments are for different time periods, equivalent capitals are calculated for a unit of time by taking,
(capital x number of units of time).
Profit or loss is divided in the ratio of these capitals.
Working partner: The partner one who works for the business is called a working partner.
Sleeping partner: The partner who simply invests the money for the business and doesn't work is called a sleeping partner.

Here first person invested amount A for $t_{1}$ period, second persons invested amount B for $t_{2}$ period and so on.

### Q1

P starts business with Rs.4500 and after 9 months, Q joins with P as his partner. After a year, the profit divided in the 3 : 5. What is Q's contribution in the capital?
A. Rs. 5,000 B. Rs. 10,000 C. Rs. 20,000 D. Rs.30,000

D
Let Q's Capital be Rs. x. Then = $\frac {4500 \times 12}{3x}$
= $\frac {4500 \times 12}{3x} = \frac {3}{5} \Rightarrow X = \frac {4500 \times 12 \times 5}{3 \times 3}$
$\Rightarrow 1500 \times 4 \times 5 \Rightarrow$ Rs. 30,000.
Hence, option D is correct.

### Q2

P and Q started a retail store with initial investments in the ratio 5 : 6 and their annual profits were in the ratio 2 : 3. If P invested the money for 8 months. For how many months did Q invest his money?
A. 5 B. 6 C. 8 D. 10

D
Suppose P invested Rs. 5x for 8 months and Q invested 6x for y months then,
$\frac {5x \times 8}{6x \times y} = \frac {2}{3} \Rightarrow y = \frac {40x \times 3}{6x \times 2}$
y = $\frac {120x}{12x} \Rightarrow y = 10$
Hence, option D is correct.

### Q3

P and Q enter into partnership. P invests some money at beginning, Q invests double the amount after 4 months and R invests thrice the amount after 8 months. If the annual profit be Rs.32000, R's share is?
A. Rs 12,000 B. Rs 15,000 C. Rs 9600 D. Rs 32,000

C
Let P's investment be Rs. x. then ratio of capitals = (x × 12) : (2x × 8) : (3x × 4)
$\Rightarrow$ 12x : 16x : 12x $\Rightarrow$ 3x : 4x : 3x
∴ R's share = Rs $[32000 \times \frac {3}{10}]$ $\Rightarrow$ Rs 9600
Hence, option C is correct.

### Q4

P, Q, R hired Taxi for Rs. 680 and used it for 3, 5, 9 hours. respectively hire charges paid by Q are:
A. Rs 100 B. Rs 200 C. Rs 300 D. Rs 350

B
P : Q : R = 3 : 5 : 9
Hire charges paid by Q
= Rs $[\frac {680 × 5}{17}]$ $\Rightarrow$ 40 × 5 = Rs 200.
Hence, option B is correct.

### Q5

In a business A and C invested amounts in the ratio 2 : 1 whereas A and B invested amounts in the ratio 3 : 2. If their annual profit be Rs. 157300, then B’s share in the profit is
A. Rs. 24200 B. Rs. 2420 C. Rs. 48000 D. Rs. 48400

D
Annual profit = 157300
A : B = 3 : 2 ⇔ 6 : 4
A : C = 2 : 1 ⇔ 6 : 3
A : B : C = 6 : 4 : 3
B's share = $\frac {4}{13} \times × 157300 = 4 × 12100 = 48400$ /-
Hence, option D is correct.