BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 3

Total Questions: 60

31. A certain sum amounts to Rs. 7,200 at the end of second year and Rs. 8,640 at the end of third year, when invested at certain rate (per annum) of compound interest compounded annually. Find the sum invested.

Correct Answer: (e) None of these
Solution:

Let the sum invested be Rs. ‘P’ and rate of interest be ‘R%’ p.a.

ATQ:
P × [1 + (R/100)]² = 7200 .......... (i)

P × [1 + (R/100)]³ = 8640 .......... (ii)

On dividing equation (ii) by equation (i), we have;
[1 + (R/100)] = 1.2

(R/100) = 0.2

R = 20

Therefore, rate of interest is 20% p.a.

On putting R = 20 in equation (i), we have;
P × [1 + (20/100)]² = 7200

P = 7200 ÷ 1.44

So, P = 5000

Therefore, the sum invested was Rs. 5,000
Hence, option e.

32. ‘A’ and ‘B’ invested Rs. 5,000 each at compound interest of 10% p.a. compounded annually and simple interest of 10% p.a., respectively. After 2 years and 3 years, ‘A’ and ‘B’, respectively invested the total amount received by them at simple interest of 20% p.a. and compound interest (compounded annually) of 20% p.a., respectively. Find the difference between the amounts with ‘A’ and ‘B’ after 5 years from the beginning.

Correct Answer: (e) Rs. 320
Solution:

For A;
Amount received after 2 years = 5000 × (1.1)²
= Rs. 6,050

Amount received after 5 years = {(6050 × 3 × 20)/100} + 6050 = Rs. 9,680

For B;
Amount received after 3 years = (5000 × 10 × 3 ÷ 100) + 5000 = Rs. 6,500

Amount received after 5 years = 6500 × (1.2)²
= Rs. 9,360

Required difference = 9680 − 9360 = Rs. 320

33. A sum is to be divided among four friends namely ‘A’, ‘B’, ‘C’ and ‘D’ such that ‘A’ received 43.75% of the sum. ‘B’ received (7/15)th of the remaining sum. The rest sum is divided between ‘C’ and ‘D’ equally. If the total sum with each of them is an integer, then which of the following could be the sum of amounts received by ‘A’ and ‘D’.

Correct Answer: (c) Rs. 2,350
Solution:

Let the total sum divided among ‘A’, ‘B’, ‘C’ and ‘D’ be Rs. ‘80x’

Sum received by ‘A’ = 0.4375 × 80x = Rs. 35x

Sum received by ‘B’ = (80x − 35x) × (7/15)
= Rs. 21x

Amount received by ‘C’ and ‘D’, each
= (80x − 21x − 35x) ÷ 2 = Rs. 12x

Sum of amounts with ‘A’ and ‘D’ = 35x + 12x
= Rs. 47x

Among the given options, only 2350 is a multiple of 47, hence ‘c’ must be the correct option.

34. A man deposited a total of Rs. 24,000, partially in scheme ‘A’ and rest in scheme ‘B’. Scheme ‘A’ offers simple interest of 12% p.a. while scheme ‘B’ offers compound interest of 20% p.a., compounded annually. At the end of 2 years, if the interest earned from scheme ‘A’ is Rs. 660 more than that from scheme ‘B’, then find the sum deposited in scheme ‘B’.

Correct Answer: (a) Rs. 7,500  
Solution:

Let the sum deposited in scheme ‘B’ be Rs. ‘x’.
So, sum deposited in scheme ‘A’ = Rs. (24000 − x)

ATQ:
[(24000 − x) × 12 × 2]/100 − [x × {(1.2)² − 1}] = 660

5760 − 0.24x − 0.44x = 660
0.68x = 5100
So, x = 7500

So, the amount deposited in scheme ‘B’
= Rs. 7,500

35. Priya invested a certain sum in scheme ‘A’ at simple interest of ‘r%’ p.a. and earned Rs. 12,600 as interest at the end of 3 years. If she had invested Rs. 15,000 in scheme ‘B’ which offers compound interest (compounded annually) of ‘r%’ p.a., then the amount fetched by her after 2 years would have been Rs. 24,576. Find the sum invested by Priya in scheme ‘A’.

Correct Answer: (c) Rs. 15,000
Solution:

According to the question,
15000 × (1 + (r/100))² = 24576

(1 + (r/100))² = (24576/15000)

(1 + (r/100))² = 1.6384

(1 + (r/100)) = 1.28

(r/100) = 0.28

r = 28

Now, let the sum invested by Priya in scheme ‘A’ be Rs. ‘p’

Therefore, {(p × 28 × 3)/100} = 12600

p = (12600/0.84)

p = 15000

Therefore, sum invested by Priya in scheme ‘A’ = Rs. 15,000

36. ‘A’ and ‘B’ started a business such that ‘A’ invested a certain amount for the entire 12 months and ‘B’ invested for ‘y’ months. If ‘B’ had invested Rs. 540 more than ‘A’, then ratio of profit shares of ‘A’ and ‘B’ would have been 3:4, respectively while if ‘B’ had invested Rs. 225 less than ‘A’, then the ratio of profit shares of ‘A’ and ‘B’ would have been 8:5, respectively. Which among the following can be determined based on the above statement?

I. Investment of ‘A’
II. Difference in between annual profit shares of ‘A’ and ‘B’
III. Time period of investment of ‘B’.

Correct Answer: (d) Only I and III
Solution:

Let the amount invested by ‘A’ = Rs. ‘K’

According to the question,
(K × 12) : {(K + 540) × y} = 3 : 4

12K : (K + 540)y = 3 : 4

48K = 3yK + 1620y – [equation 1]

Also, (K × 12) : {(K − 225) × y} = 8 : 5

12K : (K − 225)y = 8 : 5

60K = 8yK − 1800y – [equation 2]

Multiplying [equation 1] by ‘5’ and [equation 2] by ‘4’, we get

240K = 15yK + 8100y = 32yK − 7200y

15300y = 17yK

So, 900 = K

For I:
So, amount invested by ‘A’ = Rs. 900
Therefore, statement I can be determined.

For II:
Since annual profit amount is not given, the difference between annual profits of ‘A’ and ‘B’ cannot be determined.
Therefore, statement II cannot be determined

For III:
We have,
(900 × 12) : {(900 + 540) × y} = 10800 : 1440y
= 3 : 4

(1440y/4) = (10800/3)

So, 360y = 3600

So, y = (3600/360) = 10

So, time period of investment of ‘B’ can be determined
Therefore, statement III can be determined.

37. Quantity I: Tina invested a certain amount in simple interest at the rate of 18% per annum for 5 years and Meena invested the same amount in a compound interest scheme at the rate of 15% per annum for 2 years. If the interest received by Tina from the simple interest scheme is Rs.3176.25 more than the interest received by Meena, then find the sum invested by Tina?

Quantity II: Saina invests Rs.x in a simple interest scheme at the rate of 16% per annum for 4 years and he also invests Rs.4500 in another simple interest scheme at the rate of 18% per annum for 3 years. If the interest he gets from the first scheme is Rs.770 more than that of the interest received from the second scheme, and then find the value of x?

Correct Answer: (a) Quantity I > Quantity II
Solution:

From quantity I,

SI = P × N × R/100

(P × 18 × 5/100) − (P × (1 + 15/100)² − P) = 3176.25

0.9P − 0.3225P = 3176.25

P = 5500

From quantity II,

(x × 16 × 4/100) − 4500 × 18 × 3/100 = 770

0.64x = 3200

x = 5000

Quantity I > quantity II

38. Kavya invested an amount of Rs.p at the compound interest rate of 16% for 2 years and Bhavya invested Rs.(p + 800) at the simple interest rate of 9% for 3 years. If they received the same interest amount, then find the value of p.

Correct Answer: (e) None of these
Solution:

Interest received by Kavya = p(1 + 16/100)² − p

Interest received by bhavya = ((p + 800) × 9 × 3)/100

ATQ

p(1 + 16/100)² − p = ((p + 800) × 9 × 3)/100

p × 116/100 × 116/100 − p = 27p/100 + 216

0.3456p − 0.27p = 216

p = 216/0.0756 = Rs. 2857.14

39. Ravi borrows Rs.X from Bala at 15% simple interest per annum and he adds Rs.Y of his own money and lends it to Praveen at 25% simple interest per annum. At the end of the year, after returning Bala’s dues, the net interest retained by Ravi is equal to that occurred to Bala. If Ravi lent Rs.X+3Y to Praveen at 25%, then the net interest retained by Ravi would have increased by Rs.350. If Venkat invested Rs.(X+Y+5800) at the rate of 20% p.a on compound annually, then find the total amount received by Venkat after three years.

Correct Answer: (a) Rs.17280  
Solution:

(X + Y) × 25/100 − X × 15/100 = X × 15/100

5X + 5Y = 6X

5Y = X

Y = (1/5)X

Also,

(X + 3Y) × 25/100 − (X + Y) × 25/100 = 350

25x + 75y − 25x − 25y = 35000

50y = 35000

Y = Rs. 700

X = 700 × 5 = Rs. 3500

Venkat invested Rs. (X + Y + 5800) =
Rs. (3500 + 700 + 5800) = Rs. 10000

Total amount received by Venkat after 3 years
= 10000 × (120/100) × (120/100) × (120/100)
= Rs. 17280

40. M borrows Rs.8000 at simple interest from the bank. At the end of three years he again borrows Rs.3000 and closes his account after paying Rs.6715 as interest after 8 years from the time he made the first borrowing. Find the rate of interest?

Correct Answer: (a) 8.5  
Solution:

Let interest rate is r%

So, we can say,
8000 × 3 × r/100 + 11000 × r × 5/100 = 6715

240r + 550r = 6715

790r = 6715

r = 8.5%