Partnership Questions FOR Bank Exams with Detailed Solutions

Information Given:

A invested Rs. 8000, B invested Rs. 12000

A left the business after 7 months

Total profit at the end of the year = Rs. 3500

Asked: Profit share of B

Concept/Formula Used:

Profit share is proportional to Investment × Time

Profit share of B = (B’s effective capital/Total effective capital) × Total profit

Explanation:

Profit sharing ratio of A to that of B = 8000 × 7 : 12000 × 12 = 56000 : 144000

= 7 : 18

B’s profit share = $$\frac{18}{7 + 18} \times 3500$$ 

= $$\frac{18}{25} \times 3500 = 2520 \text{ Rs.}$$​

Information Given:
P invested 40% more than Q
P’s capital = 1.4 × Q
P stayed for X months; total business duration = 12 months
Profits: P = Rs. 5040, Q = Rs. 4800
Find X.
Concept/Formula Used:
In partnerships, Profit ∝ (Capital × Time).
Profit ratio = (P’s capital × P’s time) : (Q’s capital × Q’s time).
Explanation:
Profit ratio P:Q = 5040 : 4800 = 21 : 20.
Capital-time ratio:
P : Q = (1.4Q × X) : (Q × 12) = (1.4X) : 12.
Equate to profit ratio:
$$\frac{1.4X}{12} = \frac{21}{20}$$​

$$1.4X = \frac{12 \times 21}{20}$$​
X = 9
Short Trick:
Profit ratio = 5040 : 4800  =  21 : 20.
Set (1.4X):12 = 21:20
Cross-multiply:
20 × 1.4X = 21 × 12
28X = 252
X = 9

Let amount invested by A be Rs x then amount invested by C=Rs (x+4000)

Ratio of profit share of A, B and C = 9x : 24000 ×3 : (x+4000)×9

ATQ,

$$\frac{x}{x + 4000} = \frac{2}{3}$$ 

x=8000

Ratio of profit share of A, B and C= 2: 2: 3

Profit share of B=Rs 4000

Exam Hall Method: 

Given Information:
Initial Investments:
X = Rs. 6000, Y = Rs. 8000, Z = Rs. 5000
After 6 months: X withdraws 40% of his initial investment.
Total Profit at the end of the year = Rs. 26,700
Formula Used:
Investment Ratio = (Capital × Time Contribution)
Explanation:
Profit ratio of X: Y : Z = (6000 × 6) + (3600 × 6) : 8000 × 12 : 5000 × 12 = 24 :40:25.
Z’s Share = (25/89) × 26,700 = Rs. 7500

Exam Hall Approach

​

Information:
For X, investment = Rs. 12000 & time period of investment = 12 months, profit share = Rs 5000
For Y, investment for first ‘x’ months = Rs. 16000 & investment of (12-x) months = 16000/2=8000 Rs
Total profit = Rs 10000
Formula Used:
Profit sharing ratio = Investment × time period of investment
Explanation:
Ratio of profit share of X and Y = 12000 x 12 : {(16000x)+ 16000/2 x (12-x)}
144000 : (8000x + 96000)
18 : x+12

Exam Hall Method:

Information Given:
For X, investment = Rs P, time period of investment = 8 months
For Y, investment = Rs 1.5P , time period of investment = 10 months
Difference between profit share of X and Y = Rs 4200
Formula Used:
Profit sharing ratio = investment × time
Explanation:
Profit sharing ratio of X & Y = P×8 :1.5P×10 = 8m : 15m
ATQ,
15m-8m=4200
7m=4200
m=600
required answer = 8m = 4800

Exam Hall Approach

Given: 

Investment of A and B are Rs.4000 and Rs. X+3500

Time of investment of A =​ 8 months

Time of investment of B = 10 months

Profit received by B =  Rs.750

Total profit of Rs.1150

Formula Used:

Profit = investment x time

Explanation:

Exam Hall Approach

Information Given:
A invested Rs Y
B invested Rs (Y + 800)
Both invested for the same period
Total profit = Rs 6800
A’s profit share = Rs 3200
Asked: Find Y
Formula Used:
Profit share ratio = Investment ratio (since time is same)
A’s profit / B’s profit = A’s investment / B’s investment
Total profit = A’s profit + B’s profit
Explanation:
Profit ratio of A and B = 3200 : (6800 – 3200) = 3200 : 3600 = 8 : 9
Investment ratio of A and B = Y : (Y + 800) = 8 : 9
Cross multiply:
9Y = 8(Y + 800)
9Y = 8Y + 6400
9Y – 8Y = 6400
Y = 6400

Short Trick: 

Exam Hall Approach

Information Given:
R invests Rs. 3500
S invests Rs. 5000
Both invest for same time (one year)
Asked: Ratio of profits share of S to that of R
Concept/Formula Used:
Profit ratio = investment × time (time is same, so profit ratio = investment ratio)
Explanation:
Profit share of S : Profit share of R = S’s investment : R’s investment
= 5000 : 3500 = 10 : 7

Information Given:
Investment ratio of A and B = 3 : 2
3/10 of total profit goes to charity
A invested for 18 months, B invested for 15 months
A's total profit = Rs. 3600
Asked: Profit of B
Concept/Formula Used:
Profit share is proportional to Investment × Time
Total profit after charity = 7/10 of total profit
Explanation:
Let total profit = P
Net profit after charity =$$\frac{7}{10} \times P$$​
Ratio of investment × time for A and B: 3 × 18 : 2 × 15 = 54 : 30 = 9 : 5
A's share of profit = $$\frac{9}{14} \times \frac{7}{10}$$​× P = 3600
$$\frac{63}{140} \times P = 3600$$​
$$P = \frac{3600 \times 140}{63} = 8000$$​

B's profit =$$\frac{5}{14} \times \frac{7}{10} \times 8000 = \frac{35}{140} \times 8000$$​ = 2000 Rs.

Information Given:
Total profit = Rs. 10200
Investment ratio of A and B = 4 : 3
A invests for 6 months
B invests for 9 months
Asked: Profit share of A
Concept/Formula Used:
Profit share ratio = (Investment × Time)
Profit share of A = $$\text{Total Profit} \times \frac{A_{\text{investment}} \times A_{\text{time}}}{(A_{\text{investment}} \times A_{\text{time}}) + (B_{\text{investment}} \times B_{\text{time}})}$$​
Explanation:
Let investment of A = 4x and B = 3x
A’s investment duration = 6 months
B’s investment duration = 9 months
A = 4x × 6 = 24x
B = 3x × 9 = 27x
Profit share ratio of A : B = 24x : 27x = 24 : 27 = 8 : 9
Total profit = Rs. 10200
Profit share of A = $$\left(\frac{8}{8 + 9}\right) \times 10200$$​
= $$\frac{8}{17}$$​× 10200 = Rs. 4800

Information Given:

Abhi's capital = Rs. 2000

Bhushan's capital = Rs. 3000

Divya joined after 8 months with Rs. 4000 capitals

After 1 year, Divya's profit share = Rs. 6000

Asked: Total profit share of Abhi and Bhushan

Concept/Formula Used:

Profit Sharing Ratio = Capital × Time

Calculate profit shares proportional to their investments × time

Total profit share = Sum of profit shares of all partners

Explanation:

Time of investment for Abhi and Bhushan = 12 months

Time of investment for Divya = 4 months (since joined after 8 months)

Investment × Time for Abhi = 2000 × 12 = 24000

Investment × Time for Bhushan = 3000 × 12 = 36000

Investment × Time for Divya = 4000 × 4 = 16000

Profit share ratio = 24000 : 36000 : 16000 = 24 : 36 :16 = 3 : 4.5 : 2

Divya's share (2 parts) = Rs. 6000

1 part = 6000 / 2 = Rs. 3000

Abhi + Bhushan's share = (3 + 4.5) parts = 7.5 parts

Total share of Abhi and Bhushan = 7.5 × 3000 = Rs. 22500

Short Trick:

Calculate investment × time for all; ratio 3:4.5:2

Divya's 2 parts = 6000 → 1 part = 3000

Abhi and Bhushan combined = 7.5 parts

7.5 × 3000 = Rs. 22500