BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 3

Total Questions: 60

41. Rajesh invested Rs. 2500 each in two Schemes A and B for ___ years and 2 years respectively. Scheme A offers 20% p.a. Simple interest while scheme ‘B’ offers % p.a. compound interest, compounded annually. The difference between the amounts received from the two schemes is Rs.. The values are given in which of the following options will fill the blanks in the same order in which it is given to make the Statement true:

I. 6, 12, 2364  II. 8, 15, 3193.75  III. 5, 20, 1800

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

For statement I:

Amount received from scheme ‘A’ = (2500 × 20 × 6)/100 + 2500 = Rs. 5500

Amount received from scheme ‘B’
= 2500(1 + 12/100)² = Rs. 3136

The required difference = 5500 − 3136
= Rs. 2364

Therefore, the statement I is true.

For statement II:

Amount received from scheme ‘A’
= (2500 × 20 × 8)/100 + 2500 = Rs. 6500

Amount received from scheme ‘B’ = 2500(1 + 15/100)² = Rs. 3306.25

The required difference = 6500 − 3306.25
= Rs. 3193.75

Therefore, statement II is true.

For statement III:

Amount received from scheme ‘A’
= (2500 × 20 × 5)/100 + 2500 = Rs. 5000

Amount received from scheme ‘B’
= 2500(1 + 20/100)² = Rs. 3600

The required difference = 5000 − 3600 = Rs. 1400

Therefore, statement III is false.

42. A sum of the money becomes Rs.5580 after 2 years when invested in scheme A which offers simple interest and the same sum of money becomes Rs.6120 after 3 years when invested in scheme B which offers simple interest. What is the interest earned a person if he invested the same money in scheme C which offers compound interest for 2 years at the rate of 10% per annum?

Correct Answer: (a) Rs.945  
Solution:

SI = P × N × R/100
5580 − P = P × 2 × R/100
6120 − P = P × 3 × R/100

5580 − P/2 = 6120 − P/3
16740 − 3P = 12240 − 2P
P = 4500

CI = 4500 × (1 + 10/100)² − 4500
CI = 4500 × (21/100)
CI = 945

43. A person invested a sum of the amount at the rate of 12% SI per annum for two years and received a total amount of Rs.74400. He invested the same sum at the rate x % per annum compounded annually for two years and he received interest Rs.4950 more as compared to the Simple interest, find the value of ‘x’.

Correct Answer: (b) 15 %  
Solution:

Let us take the sum be x,
Given,
(124/100) × x = 74400

x = 74400 × (100/124) = Rs. 60000

S.I = 74400 − 60000 = Rs. 14400
C.I = 14400 + 4950 = Rs. 19350

Total amount = 19350 + 60000 = Rs. 79350

60000 × (1 + x/100)² = 79350

(1 + x/100)² = 529/400

(1 + x/100)² = (23/20)²

1 + x/100 = 23/20

(100 + x)/100 = 23/20

100 + x = 115

x = 15

44. A person invested a sum of the amount at the rate of 10 % SI per annum for 4 years and received a total amount of Rs. 56000. He invested the same sum at the rate of x % per annum compounded annually for two years and he received interest Rs. 1344 less as compared to the simple interest for 2 years. Then find the value of x?

Correct Answer: (b) 8  
Solution:

P + [(P × 4 × 10)/100] = 56000

(140P/100) = 56000

P = (56000 × 100)/140 = Rs. 40000

SI for 2 years = (40000 × 10 × 2)/100 = Rs. 8000

CI for 2 years = 8000 − 1344 = Rs. 6656

Total amount = 40000 + 6656 = Rs. 46656

Given,
46656 = 40000 × (1 + x/100)²

(46656/40000) = [(100 + x)/100]²

(729/625) = [(100 + x)/100]²

(27/25)² = [(100 + x)/100]²

27/25 = (100 + x)/100

108 = 100 + x

x = 108 − 100 = 8

The value of x = 8%

45. Satish invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest and he received total interest of Rs 3830 for one year. If he had interchanged the amount invested, he would have received Rs 40 more as total interest. How much did he invest at 12% simple interest initially?

Correct Answer: (a) Rs.16500  
Solution:

Let satish invests Rs X at 12% and Rs Y at 10%

Now,
X × 12/100 + Y × 10/100 = 3830
6X + 5Y = 191500 --------(i)

And, X × 10/100 + Y × 12/100 = 3830 + 40 = 3870
5X + 6Y = 193500 --------(ii)

From eq. (i) & (ii)

36X + 30Y = 1149000
25X + 30Y = 967500

11X = 181500

X = 181500/11

X = Rs.16500

46. Arun had a total of Rs. 48000 with him initially. He invested a part of his amount at 24% simple interest per annum for 5 years and the remaining at 20% compound interest for 3 years. Find what fraction of the total amount he invested in simple interest, if the total interest earned by Arun is Rs. 44384.

Correct Answer: (b) 5/12  
Solution:

Let the money invested under compound interest = a
So, money invested under simple interest = (48000 − a)

Total interest received by Arun
= a × (1.23 − 1) + (48000 − a) × 0.24 × 5

Now, (0.728a − 1.2a + 57600) = 13216

0.472a = 13216

So, value of a = 13216/0.472 = 28000

So, money invested under SI = 48000 − 28000 = Rs. 20000

Required fraction = 20000/48000 = 5/12

Hence, the answer is option B

47. Directions (47-51): Study the information and answer the following question.

Five persons invest different amounts in different schemes. Their rate of interest and type of interest is also different. Some information is given in the table.

Person  Rate of interest  Time (years)  Principal (Rs.)  Amount (Rs.)  Type of interest

A                  10%        18000      Simple
B                  6%          30000      Compound
C      5          28800            Simple
D      3                   45000      Simple
E                  12%        20000      Compound
F      2                   60000      Simple

Ques. What will be the difference of interest received by A and C if they invest for the same time and the rate of interest for C is 12%?

Correct Answer: (e) 1800
Solution:

Interest received by A = 18000 × 10 × 5/100 = 9000

Let the principle of C = x

So, interest = x × 12 × 5/100 = 0.6x

So, x + 0.6x = 1.6x = 28800

So, x = 18000

So, the interest received by C = 28800 − 18000 = 10800

So, the interest difference = 10800 − 9000 = 1800

48. Total amount received by D is what percent of the total amount received by F, if the rate of interest of D is half of E and the rate of interest of F is twice of B?

Correct Answer: (d) 71.37%  
Solution:

Amount received by
D = 45000 + 4500 × 3 × 6/100 = 53100

Amount received by
F = 60000 + 60000 × 2 × 12/100 = 74400

Required percentage = (53100/74400) × 100 = 71.37%

49. Principle of C is Rs.16500 and the amount received by D is 58500.

Quantity I: Rate of Interest of C?
Quantity II: Rate of Interest of D?

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

Quantity I:
Principle of C = 16500

So, 28800 − 16500 = 16500 × 5 × r/100

123 × 20/165 =

r = 14.909%

Quantity II:
Interest received by D = 58500 − 45000 = 13500

So, 13500 = 45000 × r × 3/100

r = 10%

Quantity I > Quantity II

50. Find the average principle of all the persons, if the rate of interest of C is 13%? (Take the approx value of C’s principle)

Correct Answer: (b) 31742.5  
Solution:

Let principle of C is x

So, x × 13 × 5/100 = 0.65x

So, 1.65x = 28800

x = 28800/1.65 = 17454.54 = 17455

So, the average principle =
[18000 + 30000 + 17455 + 45000 + 20000 + 60000]/6
= 31742.5