BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 3

Total Questions: 60

21. An amount is invested equally in two schemes (A and B). Scheme A offers 8% simple interest while Scheme B offers 10% interest rate compounded annually. Interest earned from scheme A after 3 years is Rs. 375 more than the interest earned from scheme B after 2 years. Find the amount invested in each scheme.

Correct Answer: (c) Rs. 12500
Solution:

Let the amount invested in each scheme be Rs ‘x’.
Interest earned after 3 years from scheme A
= x × 8% × 3 = Rs. 0.24x

Interest earned after 2 years from scheme B
= x × [(1.1)² − 1] = Rs. 0.21x

According to question,
0.24x − 0.21x = 375
0.03x = 375
x = 375/0.03
x = Rs. 12500

22. Directions [22-24]: Read the information given in paragraph carefully and answer the following questions.

Mahesh has a certain amount with him, out of which, 20% he invests in mutual fund, 15% he spent on shopping and 25% on rent and food. Out of remaining amount, he invested 41(2/3)% in scheme A for 2 years which offers 20% of annual compound interest and remaining in scheme B for 2 years that offers 20% simple rate of interest. If total amount of interest received from both the schemes together is Rs.2500 more than the amount spent on shopping. From the interest he obtained from scheme B he purchased some tables and some chairs. Total units (both chair and table) purchased by him is 16 and probability of selecting 2 chairs at random is 11/20. From the interest received from scheme A he purchased another item X at 16(2/3)% discount.

Ques. If two items are selected at random among purchased chairs and tables by Mahesh, then what is the probability that both the items are either tables or one is chair and another is table?

Correct Answer: (d) 9/20  
Solution:

Let the amount with Mahesh = 100x

Amount invested in mutual funds = 20% of 100x = 20x

Amount spent on shopping = 15% of 100x = 15x

Amount spent on food and rent = 25% of 100x = 25x

Remaining amount = 100x − (20x + 15x + 25x) = 40x

Amount invested in scheme A = 41(2/3)% of 40x = (50x/3)

Amount invested in scheme B = 40x − (50x/3) = (70x/3)

Amount of interest from scheme A = (50x/3) × [(1.2)² − 1] = (50x/3) × 0.44 = (22x/3)

Amount of interest from scheme B = [(70x/3) × 20 × 2]/100 = (28x/3)

Total interest received = (22x/3) + (28x/3) = (50x/3)

According to question,
(50x/3) − 15x = 2500
(5x/3) = 2500
x = 1500

Amount of interest from scheme A = (22x/3) = Rs. 11000

Amount of interest from scheme B = (28x/3) = Rs. 14000

Let number of chairs and tables purchased by him is ‘a’ and ‘16 − a’ respectively.

Probability of selecting 2 chairs at random
= ⁴C₂ / ¹⁶C₂ = 11/20

[a(a − 1)/2] / 120 = 11/20
a(a − 1) = 11 × 12 = 12 × (12 − 1)
a = 12

Number of chairs purchased by him = a = 12
Number of tables purchased by him = (16 − a) = 4

From the interest received from scheme A he purchased another item X at 16(2/3)% discount.

So, selling price of item X = Rs. 11000
Marked price of item X = 11000 × (100/83.33) = Rs. 13200

Number of chairs purchased by him = a = 12
Number of tables purchased by him = 4

Probability that both the items are tables = ⁴C₂ / ¹⁶C₂ = 1/20

Probability that one is chair and another is table = (⁴C₁ × ¹²C₁) / ¹⁶C₂ = 2/5

Required probability = (1/20) + (2/5) = 9/20

23. If marked up per cent on item X was 32% and shopkeeper sold the same item to another customer Suresh at 15% profit, then what is the discount per cent offered by shopkeeper to Suresh on that item?

Correct Answer: (a) 12 29/33%  
Solution:

Cost price of item X = 13200 × (100/132) = Rs. 10000

Selling price of item X when sold to Suresh = 115% of 10000 = Rs. 11500

Amount of Discount offered = 13200 − 11500 = Rs. 1700

Per cent of discount offered = (1700/13200) × 100 = 12(29/33)%

24. If from the interest received from scheme A, Mahesh started a business with Sunil who invested Rs.9000 and after 4 years from the start of business, Mahesh withdraws Rs.7000 and total profit amount from the business at the end of 7 years is Rs.21250, then what is the profit amount received by Sunil?

Correct Answer: (b) Rs.11250  
Solution:

Invested capital of Mahesh = Rs. 11000
Invested capital of Sunil = Rs. 9000

Ratio of their profit = (11000 × 4 + 4000 × 3) : (9000 × 7)
= 56 : 63 = 8 : 9

Profit amount received from Sunil
= 21250 × (9/17) = Rs. 11250

25. A took a loan of Rs. X from B at r% per annum compound interest for 2 years. A invested the whole amount in a scheme for 2 years. In the scheme, the amount doubles if A wins and receives only 60% of the invested amount if he loses. In this scheme, A loses and he returns the amount to B along with some of the money from the new loan that he took from C at 20% per annum simple interest and A reinvest the remaining amount in the scheme. After two more years, A paid Rs. 4,20,000 and gained Rs. 64,400. What can be the value of X and r?

Correct Answer: (b) X = Rs. 80000, r = 15%
Solution:

Total amount received by A at the end of 4th year
= 420000 + 64400 = Rs. 484400

Amount invested by A in the scheme the second time
= 484400/2 = Rs. 242200

Amount A took from C at 20% simple interest
= 420000/(1 + 20 × 2/100) = Rs. 3,00,000

Amount A returned to B from the loan he took from C
= 300000 − 242200 = Rs. 57800

Total amount to be returned to A at the end of 2 years
= 60x/100 + 57800

X × (1 + r/100)² = 60X/100 + 57800

X × (0.4 + r²/10000 + 2r/100) = Rs. 57800

Putting the values of X and r in the equation,

Option (a),
90000 × (0.4 + 144/10000 + 24/100) = 58896

Option (b),
80000 × (0.4 + 225/10000 + 30/100) = 57800

Option (c),
100000 × (0.4 + 100/10000 + 20/100) = 61000

Option (d),
120000 × (0.4 + 64/10000 + 16/100) = 67968

Option (e),
120000 × (0.4 + 25/10000 + 10/100) = 60300

Therefore, option (b) matches the equation

26. A man invested Rs.25000 at R% compound rate of interest for 3 years and amount of interest received after 3 years is Rs.6800 less than the invested amount. If he invested the same amount, partial in scheme A at (R + 5)% SI and remaining in scheme B at (R + 10)% SI. Amount of interest from scheme A after 2 years is Rs.100 less than that received from scheme B after 3 years, then amount invested in scheme B is what percent of that invested in scheme A?

Correct Answer: (e) None of these
Solution:

According to question:
25000 × [(1 + R/100)³ − 1] = 25000 − 6800

[(1 + R/100)³ − 1] = 91/125

(1 + R/100)³ = 216/125 = (6/5)³

(1 + R/100) = 6/5
R = 20%

Let amount invested in scheme A and B is ‘A’ and ‘25000 − A’ respectively.

According to question: [(A × 25 × 2)/100] + 100 = [(25000 − A) × 30 × 3]/100

5A + 1000 = 9(25000 − A)
5A + 1000 = 225000 − 9A
14A = 224000
A = 16000

Amount invested in scheme A = Rs. 16000
Amount invested in scheme B = Rs. 9000

Required per cent = (9000/16000) × 100 = 56.25%

27. Rohit invested some money at compound interest (compounded every 4 months) of 30% p.a. If 16 months later he received an amount of Rs.1,75,692, then find the sum invested by Rohit.

Correct Answer: (d) Rs. 1,20,000  
Solution:

Let the sum invested be Rs. ‘P’
Effective rate of interest = (30/12) × 4 = 10%
Effective time = 16 ÷ 4 = 4 terms of 4 months each

ATQ:
175692 = P × [1 + (10/100)]⁴
175692 = P × (11/10)⁴
175692 × (100/121) × (100/121) = P

So, P = 1,20,000
Therefore, Rohit invested Rs. 1,20,000

28. The interest earned on investing Rs. 5,500 for 3 years at compound interest of ‘y%’ p.a., compounded annually, is Rs. 4,004. What will be the interest earned on investing Rs. 6,250 for 4 years at simple interest of (y − 8)% p.a.?

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

According to the question,
5500 × [1 + (y/100)]³ − 5500 = 4004

5500 × [1 + (y/100)]³ = 5500 + 4004 = 9504

[1 + (y/100)]³ = (9504/5500) = 1.728

(1 + (y/100)) = (1.728)^(1/3) = 1.2

(100 + y) = 100 × 1.2 = 120

So, y = 120 − 100 = 20

So, simple interest earned
= 6250 × (20 − 8) × 4 ÷ 100
= 6250 × 48 ÷ 100 = Rs. 3,000

29. The compound interest earned on investing Rs. 8,000 for 2 years at compound interest of 15% p.a., compounded annually is Rs. ____ more/less than the simple interest earned on investing Rs. 4500 for 4 years at simple interest of __% p.a.

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

I. 1200, 8%  II. 1500, 6%  III. 300, 16%

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

Compound interest earned
= 8000 × [1 + (15/100)]² − 8000 = Rs. 2,580

From I:
Simple interest earned = (4500 × 8 × 4) ÷ 100
= Rs. 1,440

So, difference in interests earned = 2580 − 1440 = Rs. 1,140 ≠ Rs. 1,200
So, I is not true.

From II:
Simple interest earned = (4500 × 6 × 4) ÷ 100
= Rs. 1,080

So, difference in interest = 2580 − 1080 = Rs. 1,500
So, II is true.

From III:
Simple interest earned = (4500 × 16 × 4) ÷ 100
= Rs. 2,880

So, difference in interest = 2880 − 2580 = Rs. 300
So, III is true.

Hence, option c.

30. Ajay invested Rs. ‘P’ in scheme ‘A’ which offers compound interest of 15% p.a., compounded annually and Rs. ‘P’ in scheme ‘B’ which offers compound interest of 15% p.a., compounded after every 4 months. At the end of 1 year, the difference between the amounts received by Ajay from scheme ‘A’ and ‘B’ after 1 year is Rs. 122, then find the value of ‘P’.

Correct Answer: (c) 16000
Solution:

Effective rate of interest for scheme ‘B’ = 15 ÷ 3 = 5%
Effective time for scheme ‘B’ = 1 × 3 = 3 terms, where each term consist of 4 months.

ATQ:
P × (1.05)³ − P × (1.15) = 122

P × (1.05³ − 1.15) = 122

P × (1.157625 − 1.15) = 122

(7625P/1000000) = 122

P = 122 × 1000000 ÷ 7625

So, P = 16000