BANK & INSURANCE (PARTNERSHIP) PART 3

Total Questions: 45

31. Two partners A and B started a business by investing Rs. __ more and Rs. 6000 more than C respectively who joined them after __ months with an investment of Rs. __ invested for 2 months. After next __ months, C added Rs. 4000 and A withdrew Rs. 2000. After two year partnership, profit earned by A, B and C are in the ratio 56 : 7 : 44 respectively.

Which of the following options are possible to fill the blanks above in same order?

A. 4000, 8, 12000, 4
B. 6000, 12, 10000, 2
C. 2000, 6, 8000, 10
D. 3000, 4, 9000, 8

Correct Answer: (d) Only C
Solution:

Let two partners A and B started a business by investing Rs. P and Rs. 6000 more than C who joined them after Q months with an investment of Rs. R. After next S months, C added Rs.4000 and A withdrew Rs.2000.

C’s initial investment = R
A’s initial investment = P + R
B’s investment = 6000 + R

Then, profit ratio,

A : B : C
= ((P + R) × (Q + S) + (P + R − 2000) × (24 − Q − S)) : ((6000 + R) × 2) : (R × S + (R + 4000) × (24 − Q − S))

A : B : C
= (24P + 24R + 2000Q + 2000S − 48000) : (12000 + 2R) : (24R − QR − 4000Q − 4000S + 96000)

From (a):
P = 4000, Q = 8, R = 12000, S = 4

A : B : C
= (24 × 4000 + 24 × 12000 + 2000 × 8 + 2000 × 4 − 48000) : (12000 + 2 × 12000) : (24 × 12000 − 8 × 12000 − 4000 × 8 − 4000 × 4 + 96000)

= 30 : 32 : 56 = 5 : 6 : 7 : 44

So, this option is not possible.

From (b):
P = 6000, Q = 12, R = 10000, S = 2

A : B : C
= (24 × 6000 + 24 × 10000 + 2000 × 12 + 2000 × 2 − 48000) : (12000 + 2 × 10000) : (24 × 10000 − 12 × 10000 − 4000 × 12 − 4000 × 2 + 96000)

= 91 : 8 : 40 = 56 : 7 : 44

So, this option is not possible.

From (c):
P = 2000, Q = 6, R = 8000, S = 10

A : B : C
= (24 × 2000 + 24 × 8000 + 2000 × 6 + 2000 × 10 − 48000) : (12000 + 2 × 8000) : (24 × 8000 − 6 × 8000 − 4000 × 6 − 4000 × 10 + 96000)

= 56 : 7 : 44

So, this option is possible.

From (d):
P = 3000, Q = 4, R = 9000, S = 8

A : B : C
= (24 × 3000 + 24 × 9000 + 2000 × 4 + 2000 × 8 − 48000) : (12000 + 2 × 9000) : (24 × 9000 − 4 × 9000 − 4000 × 4 − 4000 × 8 + 96000)

= 44 : 5 : 38 ≠ 56 : 7 : 44

So, this option is not possible.

32. Directions (32-34): Read the data carefully and answer the following questions.

Two persons A and B started a business P with their initial capital in the ratio 4 : 5, after ‘x’ months, C also joined them with initial capital of Rs. 22500. After 10 months from the start, B left the business and total profit amount received from the business at the end of 15 months is Rs. 93000.

If difference between initial capital of A and B is ‘y’, then:
y/(15 – x) = 500 (1 < x < 4)

Profit amount received by A and C from business P is invested in another business Q where only these two are partners.

Time for which A invested is ‘x’ years less than investment period of C and difference between profit amount received by A and C from the business Q at the end of 6 years is ‘y’ rupees.

Ques. Difference between initial capital of C in business Q and A in business P lies between: (In Rs.)

Correct Answer: (b) 800 and 3200
Solution:

Ratio of initial capital of A and B is 4 : 5 and difference between their initial capital is ‘y’ which means initial capital of A and B is ‘4y’ and ‘5y’ respectively.

Initial capital of C = Rs. 22500

Profit weightage of A = 4y × 15 = 60y
Profit weightage of B = 5y × 10 = 50y
Profit weightage of C = 22500 × (15 − x)

Ratio of their profit = 60y : 50y : 22500 (15 − x)

Ratio of profit of B to C
= 50y : 22500 (15 − x)

= 50y / [22500 (15 − x)]

= 50/22500 × y/(15 − x)

Given: y/(15 − x) = 500

= 50/2250 × 500 = 25000/22500 = 10 : 9

Ratio of profit share of A and B = 60y : 50y = 6 : 5

Ratio of profit share of A, B, and C = 12 : 10 : 9

Profit of A = 93000 × (12/31) = Rs. 36000
Profit of B = 93000 × (10/31) = Rs. 30000
Profit of C = 93000 × (9/31) = Rs. 27000

Business Q:

Initial capital of A = Rs. 36000
Initial capital of C = Rs. 27000

Case 1: When x = 2
y = 500 × (15 − 2) = 6500

Since A invested his money for ‘x’ years less than that of C and business runs for total 6 years. Which means investment period of C is 6 years and investment period of A is 6 − x = 4 years

Ratio of their profit = 36000 × 4 : 27000 × 6 = 8 : 9

Total profit from the business Q
= 6500 × (8 + 9)

= Rs. 110500

Case 2: When x = 3
y = 500 × (15 − 3) = 6000

Since A invested his money for ‘x’ years less than that of C and business runs for total 6 years. Which means investment period of C is 6 years and investment period of A is 6 − x = 3 years

Ratio of their profit = 36000 × 3 : 27000 × 6 = 2 : 3

Total profit from the business Q
= 6000 × (2 + 3)

= Rs. 30000

Initial capital of C in business Q = Profit of C in business P = Rs. 27000

Case 1
x = 2, y = 6500

Initial capital of A in business P = 4y = 4 × 6500 = Rs. 26000

Difference = 27000 − 26000 = Rs. 1000

Case 2
x = 3, y = 6000

Initial capital of A in business P = 4y = 4 × 6000 = Rs. 24000

Difference = 27000 − 24000 = Rs. 3000

Hence, the difference lies between 800 and 3200.

33. What is the ratio of two possible values of product of ‘x’ and ‘y’?

Correct Answer: (a) 13 : 18
Solution:

Ratio of initial capital of A and B is 4 : 5 and difference between their initial capital is ‘y’ which means initial capital of A and B is ‘4y’ and ‘5y’ respectively.

Initial capital of C = Rs. 22500
Profit weightage of A = 4y × 15 = 60y
Profit weightage of B = 5y × 10 = 50y
Profit weightage of C = 22500 × (15 − x)

Ratio of their profit = 60y : 50y : 22500 (15 − x)

Ratio of profit of B to C
= 50y : 22500 (15 − x)

= 50y / [22500 (15 − x)]

= 50/22500 × y/(15 − x)

Given :
y/(15 − x) = 500

= 50/2250 × 500 = 25000/22500 = 10 : 9

Ratio of profit share of A and B = 60y : 50y = 6 : 5

Ratio of profit share of A, B, and C = 12 : 10 : 9

Profit of A = 93000 × (12/31) = Rs. 36000
Profit of B = 93000 × (10/31) = Rs. 30000
Profit of C = 93000 × (9/31) = Rs. 27000

Business Q:

Initial capital of A = Rs. 36000
Initial capital of C = Rs. 27000

Case 1: When x = 2

y = 500 × (15 − 2) = 6500

Since A invested his money for ‘x’ years less than that of C and business runs for total 6 years. Which means investment period of C is 6 years and investment period of A is 6 − x = 4 years

Ratio of their profit = 36000 × 4 : 27000 × 6 = 8 : 9

Total profit from the business Q
= 6500 × (8 + 9)
= Rs. 110500

Case 2: When x = 3

y = 500 × (15 − 3) = 6000

Since A invested his money for ‘x’ years less than that of C and business runs for total 6 years. Which means investment period of C is 6 years and investment period of A is 6 − x = 3 years

Ratio of their profit = 36000 × 3 : 27000 × 6 = 2 : 3

Total profit from the business Q
= 6000 × (2 + 3)
= Rs. 30000

Profit share of A from the business Q in case 1
= 6500 × 8 = Rs. 52000

Profit share of A from the business Q in case 2
= 6000 × 2 = Rs. 12000

Product of ‘x’ and ‘y’ in case 1 = 2 × 6500 = 13000
Product of ‘x’ and ‘y’ in case 2 = 3 × 6000 = 18000

Required ratio = 13000 : 18000
= 13 : 18

34. What is the profit share of A from the business Q?

Correct Answer: (d) Either Rs. 52000 or Rs. 12000
Solution:

Business P:

Ratio of initial capital of A and B is 4 : 5 and difference between their initial capital is ‘y’ which means initial capital of A and B is ‘4y’ and ‘5y’ respectively.

Initial capital of C = Rs. 22500

Profit weightage of A = 4y × 15 = 60y
Profit weightage of B = 5y × 10 = 50y
Profit weightage of C = 22500 × (15 − x)

Ratio of their profit = 60y : 50y : 22500 (15 − x)

Ratio of profit of B to C
= 50y : 22500 (15 − x)

= 50y / [22500 (15 − x)]

= 50/22500 × y/(15 − x)

Given :
y/(15 − x) = 500

= 50/2250 × 500 = 25000/22500 = 10 : 9

Ratio of profit share of A and B = 60y : 50y = 6 : 5

Ratio of profit share of A, B, and C = 12 : 10 : 9

Profit of A = 93000 × (12/31) = Rs. 36000

Profit of B = 93000 × (10/31) = Rs. 30000

Profit of C = 93000 × (9/31) = Rs. 27000

Business Q:

Initial capital of A = Rs. 36000

Initial capital of C = Rs. 27000

Case 1: When x = 2

y = 500 × (15 – 2) = 6500

Since A invested his money for ‘x’ years less than that of C and business runs for total 6 years. Which means investment period of C is 6 years and investment period of A is 6 – x = 4 years

Ratio of their profit = 36000 × 4 : 27000 × 6 = 8 : 9

Total profit from the business Q = 6500 × (8+9)

= Rs. 110500

Case 2: When x = 3

y = 500 × (15 – 3) = 6000

Since A invested his money for ‘x’ years less than that of C and business runs for total 6 years. Which means investment period of C is 6 years and investment period of A is 6 – x = 3 years

Ratio of their profit = 36000 × 3 : 27000 × 6 = 2 : 3

Total profit from the business Q = 6000 × (2+3)

= Rs. 30000

Profit share of A from the business Q in case 1

= 6500 × 8 = Rs. 52000

Profit share of A from the business Q in case 2

= 6000 × 2 = Rs. 12000

35. Anuj and Aman together started a business by investing Rs. 15,000 and Rs. 18,000, respectively. Six months later, Amar joined them by investing Rs. ‘X’. If at the end of the year, profit earned by Amar is 20% less than that by Anuj, then find the value of ‘X’.

Correct Answer: (a) 24000
Solution:

Ratio of profit shares of Anuj and Amar
= (15000 × 12) : (X × 6)

= 30000 : X

Also, let profit share of Anuj be Rs. ‘a’

Therefore, profit share of Anuj
= 0.80 × a = Rs. 0.8a

Ratio of profit shares of Anuj and Amar
= (a) : (0.8a)

= 5 : 4

ATQ:

(30000 / X) = (5 / 4)

5X = 4 × 30000

X = (120000 / 5)

So, X = 24000

36. ‘A’, ‘B’ and ‘C’ together started a business by investing Rs. 6,300, Rs. 5,600 and Rs. 8,400, respectively. If ‘A’, ‘B’ and ‘C’ invested their sum for 12 months, ‘y’ months and (y – 1) months, respectively and total profit received by ‘A’ and ‘B’ together was Rs. 10,750 out of which profit share of ‘A’ was Rs. 6,750, then find the total profit received by all three together.

Correct Answer: (a) Rs. 16,000
Solution:

Ratio of profit shares of ‘A’ and ‘B’, respectively

= (6300 × 12) : (5600 × y)

= 6750 : (10750 − 6750)

Or, 75600 : 5600y = 6750 : 4000

= 27 : 16

So, y = 16 × 75600 ÷ (27 × 5600) = 8

So, time for which ‘C’ invested his sum = 7 months

Ratio of profit share of ‘B’ and ‘C’
= (5600 × 8) : (8400 × 7)

= 16 : 21

So, profit share of ‘C’
= 4000 × (21/16) = Rs. 5,250

So, total profit earned
= 10750 + 5250
= Rs. 16,000

37. ‘A’ and ‘B’ together started a business by investing Rs. 12,000 and Rs. 10,000, respectively. Six months later, ‘A’ invested Rs. ___ more whereas ‘B’ withdrew Rs. 2,000. At the end of the year, the business made a profit of Rs. 12,000 out of which A’s share was Rs. ___.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:

I. 2,000, 7,000
II. 6,000, 7,500
III. 3,000, 7,200

Correct Answer: (a) Only II and III
Solution:

For statement I:

Ratio of profit shares of ‘A’ and ‘B’

= {(12000 × 6) + (14000 × 6)} : {(10000 × 6) + (8000 × 6)}

= 156000 : 108000

= 13 : 9

So, profit share of ‘A’ = 12,000 × (13/22) ≈ Rs. 7,090
So, ‘I’ is not true.

For statement II:
Ratio of profit shares of ‘A’ and ‘B’ = {(12000 × 6) + (18000 × 6)} : {(10000 × 6) + (8000 × 6)}
= 1,80,000 : 1,08,000 = 5 : 3

So, profit share of ‘A’ = 12000 × (5/8) = Rs. 7,500

So, ‘II’ is true.

For statement III:
Ratio of profit shares of ‘A’ and ‘B’ = {(12000 × 6) + (15000 × 6)} : {(10000 × 6) + (8000 × 6)}
= 1,62,000 : 1,08,000 = 3 : 2

So, profit share of ‘A’ = 12000 × (3/5)
= Rs. 7,200

So, ‘III’ is true

38. ‘A’ and ‘B’ together started a business by investing Rs. 4,000 and Rs. 6,000, respectively. ‘A’ also works as a manager and hence is entitled to receive 20% of the total profit as salary. The rest of the profit will be divided between ‘A’ and ‘B’ in the ratio of their investments. If the salary received by ‘A’ from the business at the end of the year is Rs. 3,000, then find the profit share of ‘B’ at the end of the year.

Correct Answer: (a) Rs. 7,200
Solution:

Ratio of profit share of ‘A’ and ‘B’ = 4000 : 6000 = 2 : 3

Total profit earned by the business = 3000 ÷ 0.20
= Rs. 15,000

Profit share of ‘B’ = (15000 − 3000) × (3/5)
= Rs. 7,200

39. ‘A’, ‘B’ and ‘C’ started a business by investing Rs. 800, Rs. 1,200 and Rs. 1,500, respectively. 6 months later, ‘A’ increased his investment by ‘x%’ while ‘B’ and ‘C’ decreased their investment by 25% and 40% such that at the end of first year, ratio of profit shares of ‘A’, ‘B’ and ‘C’ was 6:7:8, respectively. If the total profit earned from the business at the end of 2 years was Rs. 11,900, then find the profit share of ‘B’ out of it.

Correct Answer: (a) Rs. 3,900
Solution:

Let the increased investment of ‘A’ = Rs. ‘Y’

Then, ratio of profit shares of ‘A’, ‘B’ and ‘C’ at the end of 1 year

= (800 × 6 + Y × 6) : (1200 × 6 + 1200 × 0.75 × 6) : (1500 × 6 + 1500 × 0.6 × 6)

= 6 : 7 : 8

Or, (4800 + 6Y) : (12600) : (14400) = 6 : 7 : 8

(4800 + 6Y) ÷ 6 = 12600 ÷ 7 = 1800

So, Y = 1000

So, ratio of profit shares of ‘A’, ‘B’ and ‘C’ at the end of 2 years

= (800 × 6 + 1000 × 18) : (1200 × 6 + 900 × 18) : (1500 × 6 + 900 × 18)

= (22800) : (23400) : (25200)

= 38 : 39 : 42

So, profit share of ‘B’ at the end of 2 years

= 11900 ÷ (38 + 39 + 42) × 39

= Rs. 3,900

40. ‘A’ and ‘B’ started a business by investing Rs. ‘x’ and Rs. ‘x − y’, respectively. Six months later, they both increased their investments by Rs. ‘y’. If at the end of the year the business made a profit of Rs. ‘10x’, then the profit share received by ‘A’, exceeds that of ‘B’ by:

Correct Answer: (e) Rs. ‘5y’
Solution:

Ratio of profit shares of ‘A’ and ‘B’

= (6 × x × x + 6 × (x + y)) : (6 × (x − y) + 6 × x)

= (12x + 6y) : (12x − 6y)

= (2x + y) : (2x − y)

Profit share of ‘A’

= 10x × (2x + y) ÷ (2x + y + 2x − y)

= Rs. {(10x² + 5xy) / 2x}

Profit share of ‘B’

= 10x × (2x − y) ÷ (2x + y + 2x − y)

= Rs. {(10x² − 5xy) / 2x}

So, required difference

= {(10x² + 5xy)/2x} − {(10x² − 5xy)/2x}

= {(5xy + 5xy)/2x}

= Rs. 5y