BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 3

Total Questions: 60

11. Arjun and Rajiv deposited Rs. 8400 and Rs. ____ in scheme A at 20% and at 10% per annum compound interest compounded annually, respectively. Also, Arjun and Rajiv deposited Rs. ____ and Rs. 3700 in scheme B at 15% and at 24% per annum simple interest, respectively. Sum of interest earned by both from both schemes together after 2 years is 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. 7200, 4120, 8220
II. 9600, 3640, 8540
III. 8000, 5400, 8772

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

Let, amount deposited by Rajiv in scheme A and Arjun in scheme B be Rs. x and Rs. y, respectively.

Interest earned by Arjun from scheme A = 8400 × {(1.2)² − 1} = Rs. 3696

Interest earned by Rajiv from scheme A = x × {(1.1)² − 1} = Rs. 0.21x

Interest earned by Arjun from scheme B = y × 0.15 × 2 = Rs. 0.3y

Interest earned by Rajiv from scheme B = 3700 × 0.24 × 2 = Rs. 1776

So, sum of interest earned by both of them = 3696 + 0.21x + 0.3y + 1776
= Rs. 5472 + 0.21x + 0.3y

From option I:
Sum of interest = 5472 + 0.21x + 0.3y = 5472 + 0.21 × 7200 + 0.3 × 4120 = 5472 + 1512 + 1236
= Rs. 8220

So, option I can be the answer.

From option II:
Sum of interest = 5472 + 0.21x + 0.3y = 5472 + 0.21 × 9600 + 0.3 × 3640 = 5472 + 2016 + 1092
= Rs. 8580

So, option II cannot be the answer.

From option III:
Sum of interest = 5472 + 0.21x + 0.3y = 5472 + 0.21 × 8000 + 0.3 × 5400 = 5472 + 1680 + 1620
= Rs. 8772

So, option III can be the answer.

Hence, option e.

12. Directions (12-14): Answer the questions based on the information given below.

Rohit and Bumrah invested their respective sum in schemes ‘P’ and ‘Q’, respectively at compound interest, compounded annually. Rohit and Bumrah received Rs. (6x² + 40x + 76) and Rs. (4x² + 32x − 80), respectively at the end of 2 years and received Rs. (300x − 225), and Rs. 189x, respectively at the end of 3 years. ‘Ankush’, ‘Birbal’ and ‘Chetan’ entered into a business with initial investments of Rs. (x² + 5x + 16), Rs. (32x + 26) and Rs. (46x + 28), respectively. After 7 months, Ankush withdrew Rs. 130, Birbal withdrew Rs. 320 and Chetan withdrew Rs. 300 and annual profit shared by Ankush was Rs. 3600, out of total annual profit earned by them together which is Rs. 10800.

Note: Sum invested by Ankush is more than Rs. 1000.

Ques. Annual profit earned by Chetan is:

Correct Answer: (c) Rs. 4320
Solution:

Ratio of profit share of Ankush, Birbal and Chetan, respectively at the end of 1st year =
[(x² + 5x + 16) × 12 − 130 × 5] : [(32x + 26) × 12 − 320 × 5] : [(46x + 28) × 12 − 300 × 5]
= (12x² + 60x − 458) : (384x − 1288) : (552x − 1164)

ATQ:
(12x² + 60x − 458) / (12x² + 996x − 2910) = 3600/10800 = 1/3

36x² + 180x − 1374 = 12x² + 996x − 2910

24x² − 816x + 1536 = 0

x² − 34x + 64 = 0

x² − 32x − 2x + 64 = 0

x(x − 32) − 2(x − 32) = 0

(x − 2)(x − 32) = 0

So, x = 32 or x = 2

Since, amount invested by Rohit and Bumrah is more than Rs. 1500. So, x = 32

Amount received by Rohit at the end of 2 years
= 6x² + 40x + 76 = 6 × 32 × 32 + 40 × 32 + 76
= Rs. 7500

Amount received by Bumrah at the end of 2 years
= 4x² + 32x − 80 = 4 × 32 × 32 + 32 × 32 − 16
= Rs. 5040

Amount received by Rohit at the end of 3 years
= 300x − 225 = 300 × 32 − 225 = Rs. 9375

Amount received by Bumrah at the end of 3 years
= 189x = 189 × 32 = Rs. 6048

For Rohit:
Let amount invested in scheme ‘P’ be Rs. ‘p’ and rate of interest offered by scheme ‘P’ is R% p.a.

So, p(1 + R/100)² = 7500 ………… (1)
And, p(1 + R/100)³ = 9375 ………… (2)

Equation (2) ÷ Equation (1), we get
(1 + R/100) = 9375/7500 = 5/4

R/100 = 1/4
R = 25%

So, p = (7500)/(1.25 × 1.25) = Rs. 4800

For Bumrah:
Let amount invested in scheme ‘Q’ be Rs. ‘b’ and rate of interest offered by scheme ‘Q’ is T% p.a.

So, b(1 + T/100)² = 5040 ………… (1)
And, b(1 + T/100)³ = 6048 ………… (2)

Equation (2) ÷ Equation (1), we get
(1 + T/100) = 6048/5040 = 6/5

T/100 = 1/5
T = 20%

So, b = (5040/(1.20 × 1.20)) = Rs. 3500

Ratio of profit share of Ankush, Birbal and Chetan, respectively at the end of 2 years =
(12x² + 60x − 458) : (384x − 1288) : (552x − 1164)
= 13750 : 11000 : 16500 = 5 : 4 : 6

Annual profit share of Chetan = (6/15) × 10800
= Rs. 4320

13. Rate of interest offered by scheme ‘P’ is:

Correct Answer: (a) 25%  
Solution:Rate of interest offered by scheme ‘P’ = 25%.

14. Amount invested by Bumrah is:

Correct Answer: (d) Rs. 3500  
Solution:Amount invested by Bumrah = Rs. 3500

15. Vrushali invested Rs. (X + 3000) on compound interest of ‘r%’ p.a. compounded annually for 2 years and Tarushi invested Rs. (X − 2000) on simple interest of (r − 2)% p.a. for 3 years. The total interest received by both of them is Rs. 12360. If Anant invested Rs. (X + 8000) on simple interest for 3 years on 15% and received an interest of Rs. 13500, find the value of ‘r’.

Correct Answer: (c) 12
Solution:

According to the question,
Simple interest received by Anant = Rs. 13500
(X + 8000) × 15% × 3 = 13500
(X + 8000) = 30000
X = 22000

Amount invested by Vrushali = Rs. 22000 + 3000
= Rs. 25000

Amount invested by Tarushi = 22000 − 2000 = Rs. 20000

The total interest received by Vrushali and Tarushi = Rs. 12360

[25000 × (1 + r/100)² − 25000 + 20000 × (r − 2)% × 3] = 12360

25000 × (1 + r/100)² − 25000 + 600(r − 2) = 12360

25000 × (1 + r²/10000 + r/50) − 25000 + 600(r − 2) = 12360

25000 + 2.5r² + 500r − 25000 + 600r − 1200 = 12360

2.5r² + 1100r = 13560

r² + 440r − 5424 = 0

r² + 452r − 12r − 5424 = 0

r(r + 452) − 12(r + 452) = 0

(r + 452)(r − 12) = 0

r = −452, 12

Rate of interest cannot be negative. So, r = 12

16. Directions (16-18): Answer the questions based on the information given below.

Amount invested by Rohan in scheme ‘A’ and ‘B’ is in the ratio 16:9, respectively. Scheme ‘A’ offers simple interest of 36% p.a. while scheme ‘B’ offers compound interest of 20% p.a. compounded annually and total interest received by him at the end of 2 years from the given two schemes is Rs. 7740. If total amount invested by Rohan is Rs. ‘50y’, then total cost price of articles ‘P’ and ‘Q’ purchased by him is Rs. ‘21.2y’. If Rohan sold both articles to Sundar at the same price while he gained a profit of 32% on article ‘P’ and faced a loss of 20% on selling article ‘Q’. Cost price of article ‘R’ is Rs. 700 more than that of article ‘Q’ and is marked 60% above the cost price and sold after two successive discounts of (d − 10)% and (d − 15)%, respectively and profit earned on doing so is Rs. 352.

Ques. If Rs. ‘8y’ is invested at compound interest of 4% p.a. compounded annually, then find the amount received at the end of two years.

Correct Answer: (c) 2163.20
Solution:

Let amount invested by Rohan in scheme ‘A’ and ‘B’ be Rs. 16x and Rs. 9x, respectively.

So, 0.36 × 2 × 16x + 1.44 × 9x − 9x = 7740

11.52x + 3.96x = 7740

15.48x = 7740

x = 500

So, 50y = 25x = 25 × 500

y = 250

Cost price of article ‘P’ and ‘Q’ together = 21.2 × 250 = Rs. 5300

Let cost price of article ‘P’ be Rs. ‘a’
And, cost price of article ‘B’ be Rs. ‘b’

So, a + b = 5300

Selling price of article ‘P’ = 1.32 × a = Rs. 1.32a

Selling price of article ‘Q’ = 0.80 × b = Rs. 0.8b

So, 1.32a = 0.8b

a/b = 0.8/1.32 = 20/33

Cost price of article ‘P’ = (20/53) × 5300
= Rs. 2000

Cost price of article ‘Q’ = (33/53) × 5300
= Rs. 3300

Cost price of article ‘R’ = 3300 + 700 = Rs. 4000

Marked price of article ‘R’ = 1.60 × 4000 = Rs. 6400

Selling price of article ‘R’ = 4000 + 352 = Rs. 4352

Total discount given on article ‘R’ = 1.60 × 4000 − 4352 = Rs. 2048

Discount percentage on article ‘R’ = (2048/6400) × 100
= 32%

So, d − 10 + d − 15 − {(d − 10)(d − 15)/100} = 32

2d − 57 − {(d² − 25d + 150)/100} = 0

200d − 5700 − d² + 25d − 150 = 0

d² − 225d + 5850 = 0

d² − 195d − 30d + 5850 = 0

d(d − 195) − 30(d − 195) = 0

(d − 195)(d − 30) = 0

d = 30 or d = 195 (not possible)

Sum invested = 8y = 8 × 250 = Rs. 2000

Desired amount = 1.04 × 1.04 × 2000 = Rs. 2163.20

17. Selling price of article ‘P’ is:

Correct Answer: (c) Rs. 2640
Solution:Selling price of article ‘P’ = 1.32 × 2000 = Rs. 2640

18. Find the value of ‘d’.

Correct Answer: (d) 30  

19. Anup deposited Rs. (2x + 5000) in a bank which offers compound interest of 12% p.a. compounded every 4 months. His friend Ashok invested Rs. 10000 more than him in another bank which offers compound interest of 8% p.a. compounded half yearly. If Anup got Rs. 49.28 more interest than Ashok at the end of the year, then which of the following is true about ‘x’?

I. Simple interest earned on a sum of Rs. (x + 2500) for 2 years at a rate of 25% p.a. is Rs. 5000.
II. Difference between the simple and compound interest on Rs. ‘x’ for 2 years at 20% p.a. compounded annually is Rs. 300.
III. HCF of ‘x’ and (2x − 5000) is 2500.

Correct Answer: (c) All I, II and III
Solution:

For Anup,
Interest gained after the end of the year = (2x + 5000)[{(12/3)/100}³ − 1] = Rs. [(2x + 5000){(26/25)³ − 1}]

For Ashok,
Interest gained after the end of the year = (2x + 5000 + 10000)[{(8/2)/100}² − 1] = Rs. [(2x + 15000){(26/25)² − 1}]

According to the question,
[(2x + 5000){(26/25)³ − 1}] − [(2x + 15000){(26/25)² − 1}] = 49.28

1951(2x + 5000) = 1275(2x + 15000) + 770000

1352x = 1014000

x = 7500

Now,
For ‘I’:
Simple interest = {(7500 + 2500) × 2 × 25}/100
= Rs. 5000
So, ‘I’ is true.

For ‘II’:
Required difference = [{(1.2)² − 1} − 0.20 × 2] × 7500
= 0.04 × 7500 = Rs. 300
So, ‘II’ is true.

For ‘III’:
Since, 2x − 5000 = 2 × 7500 − 5000 = 10000
HCF of 7500 and 10000 = 2500
So, ‘III’ is true.

20. Anurag invested a certain amount of money in a scheme at a rate of 20% p.a. compounded annually for 2 years and received certain amount of interest. Had he invested the same amount for the same time period and rate of interest but compounded half yearly, then he would have received Rs. 482 more interest. Find the amount of money invested in the scheme.

Correct Answer: (c) Rs. 20000
Solution:

Let the certain sum of money be Rs. ‘P’.
Compound interest received when the interest is compounded annually
= P × [(1.2)² − 1] = Rs. 0.44P

Compound interest received when the interest is compounded half yearly then rate = 20/2 = 10% p.a. and time will be doubled.
So, Interest received now = P × [(1.1)⁴ − 1]
= Rs. 0.4641P

According to question,
0.4641P − 0.44P = 482
0.0241P = 482
P = Rs. 20000