BANK & INSURANCE (PARTNERSHIP) PART 2

Total Questions: 45

31. ‘A’, ‘B’ and ‘C’ started a business with initial investment of Rs. 5,000, Rs. 4,000 & Rs. 3,000, respectively. After 6 months, ‘A’ withdrew Rs. 1,000 and after 2 more months, ‘C’ invested Rs. 2,000 more into the business. Find the annual profit share of ‘A’ if total profit received from the business at the end of the year is Rs. 14,600.

Correct Answer: (e) Rs. 5,400
Solution:

Ratio of profit shares of ‘A’, ‘B’ and ‘C’
= (5000 × 6 + 4000 × 6) : (4000 × 12) : (3000 × 8 + 5000 × 4)

= 27 : 24 : 22

The share of ‘A’ in the annual profit
= (27/(27 + 24 + 22)) × 14600 = Rs. 5,400

32. ‘A’ and ‘B’ started a business by investing Rs. 5,000 and Rs. 8,000, respectively. 6 months later, ‘A’ increased his investment by Rs. 500 and 2 months after that ‘B’ decreased his investment by 75%. At the end of the year, if the profit share received by ‘A’ was Rs. 1,680, then what was the annual profit share received ‘B’?

Correct Answer: (c) Rs. 1,920
Solution:

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

= (5000 × 6 + (5000 + 500) × 6) : (8000 × 8 + 8000 × 0.25 × 4)

= (30000 + 33000) : (64000 + 8000)

= 63 : 72 = 7 : 8

So, annual profit share of ‘B’
= 1680 × (8/7)

= Rs. 1,920

33. Nidhi and Vidhi started a business by investing their capitals in the ratio of 3:4, respectively. After 6 months, Nidhi increased her investment by Rs. 500 and Vidhi decreased her investment by Rs. 600. Find the initial investment done by Vidhi if the annual profit share of Nidhi is Rs. 2,000 out of total annual profit of Rs. 4,400.

Correct Answer: (c) Rs. 6,000
Solution:

Let the initial investment done by Nidhi and Vidhi be
Rs. ‘3x’ and Rs. ‘4x’, respectively.

Profit sharing ratio of Nidhi and Vidhi

= (3x + 3x + 500) : (4x + 4x − 600)

= (6x + 500) : (8x − 600)

5 : 6 = (6x + 500) : (8x − 600)

40x − 3000 = 36x + 3000

4x = 6000

So, x = 1500

Initial investment done by Vidhi
= (1500 × 4)

= Rs. 6,000

34. ‘A’ started a business with the initial investment of Rs. 4,000. After 8 months, ‘B’ joined the business. If at the end of the year, the total profit earned from the business is divided between ‘A’ and ‘B’ in the ratio of 3:2, respectively, then find the investment of ‘B’.

Correct Answer: (b) Rs. 8,000
Solution:

Let the investment of ‘B’ be Rs. ‘x’

We know that the profit is shared in the ratio of
(investment × time)

Ratio of profit share of ‘A’ and ‘B’
= (4000 × 12) : (x × 4)

= 12000 : x

Given,

(12000/x) = (3/2)

3x = 24000

x = 8000

So, the investment of ‘B’ = Rs. 8,000

35. While starting a business, investment done by Pooja was Rs. 800 more than that by Anu. After 4 months, Anu increased her investment by 20% while Pooja decreased her investment by 25%. Find the initial investment done by Anu, if the ratio between annual profit share of Pooja and total annual profit earned from the business is 15:32, respectively.

Correct Answer: (e) Rs. 4,000
Solution:

Let the initial investment done by Anu be Rs. ‘20x’

So, initial investment done by Pooja
= Rs. (20x + 800)

According to question:

Profit sharing ratio of Anu and Pooja

= (20x × 4 + 20x × 1.2 × 8) : {(20x + 800) × 4 + (20x + 800) × 0.75 × 8}

So, {(80x + 192x) : (80x + 3200 + 120x + 4800)}

= (17/32 : 17)

(272x) : (200x + 8000) = (17/15)

{16x/(200x + 8000)} = (1/15)

25x + 1000 = 30x

5x = 1000

x = 200

So, initial investment done by Anu
= 20x = 20 × 200

= Rs. 4,000

36. ‘A’ and ‘B’ started a business by investing Rs. ‘x’ and Rs. ‘x + 650’, respectively. Four months later, ‘A’ doubled his investment. If at the end of the year, the profit share of ‘A’ was Rs. 30,000 out of total profit of Rs. 74,000, then find the amount invested by ‘B’.

Correct Answer: (c) Rs. 1,100
Solution:

Profit share of ‘B’ = 74000 − 30000 = Rs. 44,000

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

= {(x × 4) + (2x × 8)} : {(x + 650) × 12}

= 20x : (12x + 7800)

ATQ:

20x/(12x + 7800) = (30000/44000)

44 × 2x = 3 × (12x + 7800)

88x = 36x + 23400

52x = 23400

So, x = 450

So, amount invested by ‘B’
= 450 + 650 = Rs. 1,100

37. ‘A’ and ‘B’ started a business by investing Rs. ‘x + 1800’ and Rs. ‘2x’, respectively. Four months later, ‘A’ withdrew half of his investment. If at the end of the year, the profit share of ‘B’ was Rs. 24,000 out of total profit of Rs. 44,000, then find the initial investment of ‘A’.

Correct Answer: (e) Rs. 3,000
Solution:

Profit share of ‘A’ = 44000 − 24000 = Rs. 20,000

Ratio of profit shares of ‘A’ and ‘B’

= {(x + 1800) × 4 + {(x/2) + 900} × 8} : (2x × 12)

= (8x + 14400) : (24x)

ATQ:

{8(x + 1800)/24x} = (20000/24000)

(x + 1800) × 6 = 3x × 5

6x + 10800 = 15x
9x = 10800
So, x = 1200

So, initial investment of ‘A’ = 1200 + 1800 = Rs. 3,000

38. ‘A’ and ‘B’ started a business together where ‘B’ invested Rs. 200 more than ‘A’. ‘A’ withdrew his entire investment after 8 months. If the total annual profit earned from the business was Rs. 9,700 out of which the profit share of ‘B’ was Rs. 2,900 more than that of ‘A’, then find the initial investment of ‘A’.

Correct Answer: (b) Rs. 850
Solution:

Let the profit share of ‘A’ = Rs. ‘K’

Then, profit share of ‘B’ = Rs. (K + 2900)

We have,
K + K + 2900 = 9700

2K + 2900 = 9700

K = (9700 − 2900) ÷ 2 = 3400

So, Profit shares of ‘A’ and ‘B’ are Rs. 3,400 and Rs. 6,300, respectively

So, ratio of profit shares of ‘A’ and ‘B’ = 3400 : 6300
= 34 : 63

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

Then, initial investment of ‘B’ = Rs. (Y + 200)

Ratio of profit shares of ‘A’ and ‘B’

= (Y × 8) : ((Y + 200) × 12) = 8Y : (12Y + 2400)

= 34 : 63

504Y = 408Y + 81600

So, Y = 81600 ÷ 96 = 850

39. Arvind and Amit started a business with initial investments of Rs. 4000 and Rs. 6000, respectively. After t months, Arvind withdrew 1/5th of his initial investment and Amit withdrew 11/20th of his initial investment while Ajay entered into the business investing Rs. 9100. If total profit earned at the end of 2 years is Rs. 72000 and profit share of Arvind is Rs. 19200, then find the profit share of Ajay?

Correct Answer: (b) Rs. 31200
Solution:

Ratio of profit share of Arvind, Amit and Ajay, respectively

= [4000 × t + 0.80 × 4000 × (24 − t)] : [6000 × t + 0.45 × 6000 × (24 − t)] : [9100 × (24 − t)]

= [8t + 768] : [33t + 648] : [2184 − 91t]

According to question,

(8t + 768) / (3600 − 50t) = 19200 / 72000 = 4 / 15

120t + 11520 = 14400 − 200t

320t = 2880

t = 9

Profit share of Arvind, Amit and Ajay, respectively

= [8 × 9 + 768] : [33 × 9 + 648] : [2184 − 91 × 9]

= 840 : 945 : 1365 = 8 : 9 : 13

Profit share of Ajay = 13/30 × 72000 = Rs. 31200

40. A total of Rs 84,000 is invested in a business. Investment of A is Rs 4000 less than that of B and B’s investment is Rs 4000 less than that of C. If A invested his amount for 5 months and B and C each for 4 months, then out of total profit of Rs 63,000 what is the share of A?

Correct Answer: (a) Rs 21,000
Solution:

Let C’s investment is Rs x, then B’s = Rs (x − 4000), then A’s = Rs (x − 4000 − 4000)

= Rs (x − 8000)

So (x − 8000) + (x − 4000) + (x) = 84000

Solve, x = 32,000

So ratio of shares of A, B and C is

24000 × 5 : 28000 × 4 : 32000 × 4

= 15 : 14 : 16

So A’s share = 15/(15 + 14 + 16) × 63000

= Rs 21000