Simple and Compound Interest Questions for RRB-NTPC Set-3 PDF

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Simple and Compound Interest Questions PDF

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Question 1: What is the difference (in Rs) between compound interest (compounded annually) and simple interest for 3 years on a principal of Rs 3000 at the annual rate of 20% ?

a) 464

b) 384

c) 356

d) 424

Question 2: The difference between simple interest on a certain sum at the rate of 8% per annum for 18 months and 24 months is Rs 452. What is the sum (in Rs)?

a) 10500

b) 14600

c) 11300

d) 13600

Question 3: Simple interest on a sum for 10 years is equal to 5% of the principal. In how many years interest will be equal to the principal?

a) 100

b) 150

c) 200

d) 250

Question 4: A sum of money invested at simple interest becomes $\frac{13}{10}$ of itself in 2 years and 6 months. What is the rate (in percentage) of interest per annum?

a) 10

b) 15

c) 12

d) 18

Question 5: The simple interest on a sum of money is $\frac{16}{25}$ of the principal. The number of years is equal to the rate of interest per annum. What is the rate (in percentage) of interest per annum?

a) 4

b) 16

c) 8

d) 12

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Question 6: A sum of Rs 5000 becomes Rs 8000 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of interest is yearly), then what will be the amount (in Rs) after 3 years?

a) 8640

b) 8260

c) 8880

d) 9220

Question 7: The simple interest on a sum is $\frac{5}{9}$ of the principal for 25 years. What is the rate (in percentage) of interest per annum?

a) $\frac{25}{9}$

b) $\frac{9}{2}$

c) $\frac{20}{9}$

d) $\frac{15}{4}$

Question 8: Simple interest on a sum of Rs 67400 for 14 months is Rs 4718. What is the rate (in percentage) of interest per annum?

a) 5.5

b) 6

c) 8

d) 7

Question 9: Some part of Rs 17500 was lent at the rate of 24% per annum simple interest and the remaining part at the rate of 10% per annum simple interest. The total interest received after 5 years is Rs 13300. What is the ratio of money lent at the rate of 24% and 10%?

a) 12 : 13

b) 3 : 4

c) 3 : 2

d) 13 : 22

Question 10: A sum of Rs 4000 becomes Rs 5800 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of interest is done yearly), then what will be the amount (in Rs) after 2 years?

a) 4430

b) 5450

c) 5290

d) 4970

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Question 11: The difference between the simple interest and compound interest (compounded annually) on Rs. 40,000 for 3 years at 8% per annum is

a) Rs.684.32

b) Rs.788.48

c) Rs.784.58

d) Rs.4000

Question 12: The difference between compound interest and simple interest on a certain sum of money for 2 years at 5% per annum is Rs. 41. What is the sum of money?

a) Rs.7200

b) Rs.9600

c) Rs.16400

d) Rs.8400

Question 13: The difference between simple and compound interest (compounded annually) on a sum of money for 3 years at 10% per annum is Rs. 93. The sum (in Rs.) is:

a) 30000

b) 30300

c) 3000

d) 3030

Question 14: The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525 . The simple interest on the same sum for double the time at half the rate percent per annum is :

a) Rs.520

b) Rs.550

c) Rs. 500

d) Rs. 515

Question 15: The compound interest on Rs. 64,000 for 3 years, compounded annually at 7.5% p.a. is

a) Rs. 14,400

b) Rs. 15,705

c) Rs. 15,507

d) Rs. 15,075

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Question 16: The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is?

a) 6%

b) 7%

c) 8%

d) 9%

Question 17: The amount of Rs. 10,000 after 2 years, compounded annually with the rate of interest being 10% per annum during the first year and 12% per annum during the second year, would be (in rupees)

a) 11,320

b) 12,000

c) 12,320

d) 12,500

Question 18: The difference between the compound interest and the simple interest on Rs. 6250 at 8% per annum in 2 years is

a) Rs.30

b) Rs.40

c) Rs.50

d) Rs.60

Question 19: The difference between compound interest and simple interest on Rs. 5000 for 2 years at 8% per annum payable yearly is

a) Rs.30

b) Rs.31

c) Rs.33

d) Rs.32

Question 20: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum (in Rs.) is:

a) 620

b) 630

c) 640

d) 625

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Answers & Solutions:

1) Answer (B)

Principal sum = Rs. 3,000

Rate of interest = 20% and time period = 3 years

=> Difference between compound and simple interest = $[P(1+\frac{R}{100})^T-P]-(\frac{P \times R\times T}{100})$

= $[3000(1+\frac{20}{100})^3-3000]-(\frac{3000 \times 20\times 3}{100})$

= $[3000(\frac{6}{5})^3-3000]-(1800)$

= $3000\times(\frac{216}{125})-4800$

= $(24\times216)-4800$

= $5184-4800=Rs.$ $384$

=> Ans – (B)

2) Answer (C)

Let the sum be = Rs. $100x$

Rate of interest = 8%

=> Simple interest = $\frac{P\times R\times T}{100}$

According to ques,

=> $(\frac{100x\times8\times2}{100})-(\frac{100x\times8\times1.5}{100})=452$

=> $16x-12x=452$

=> $x=\frac{452}{4}=113$

$\therefore$ Sum = $100\times113=Rs.$ $11,300$

=> Ans – (C)

3) Answer (C)

Let principal amount = Rs. $100x$

=> Simple interest = $\frac{5}{100}\times100x=Rs.$ $5x$

Let rate of interest = $r\%$ and time period = 10 years

=> Simple interest = $\frac{P\times R\times T}{100}$

=> $\frac{100x\times r\times10}{100}=5x$

=> $10r=5$

=> $r=\frac{5}{10}=0.5\%$

Let the interest will be equal to the principal in = $t$ years at 0.5% rate

=> $\frac{100x\times 0.5\times t}{100}=100x$

=> $t=\frac{100}{0.5}=200$ years

=> Ans – (C)

4) Answer (C)

Let sum of money invested = Rs. $100x$

=> Amount under simple interest = $\frac{13}{10}\times100x=Rs.$ $130x$

Thus, simple interest = $130x-100x=Rs.$ $30x$

Let rate of interest = $r\%$ and time period = 2.5 years

=> Simple interest = $\frac{P\times R\times T}{100}$

=> $\frac{100x\times r\times2.5}{100}=30x$

=> $2.5r=30$

=> $r=\frac{30}{2.5}=12\%$

=> Ans – (C)

5) Answer (C)

Let sum of money invested = Rs. $100x$

=> Simple interest = $\frac{16}{25}\times100x=Rs.$ $64x$

Let rate of interest = time period = $x$

=> Simple interest = $\frac{P\times R\times T}{100}$

=> $\frac{100x\times x\times x}{100}=64x$

=> $x^2=64$

=> $x=\sqrt{64}=8\%$

=> Ans – (C)

6) Answer (A)

Principal sum = Rs. 5000 and time period = 3 years

=> Amount after simple interest = Rs. 8000

Thus, simple interest = Rs. (8000-5000) = Rs. 3000

Let rate of interest = $r\%$

=> Simple interest = $\frac{P\times R\times T}{100}$

=> $\frac{5000\times r\times3}{100}=3000$

=> $150r=3000$

=> $r=\frac{3000}{150}=20\%$

$\therefore$ Amount under compound interest = $P(1+\frac{R}{100})^T$

= $5000(1+\frac{20}{100})^3$

= $5000(1+\frac{1}{5})^3=5000(\frac{6}{5})^3$

= $5000\times\frac{216}{125}$

= $40\times216=Rs.$ $8640$

=> Ans – (A)

7) Answer (C)

Let principal amount = Rs. $9x$

=> Simple interest = $\frac{5}{9}\times9x=Rs.$ $5x$

Let rate of interest = $r\%$ and time period = 25 years

=> Simple interest = $\frac{P\times R\times T}{100}$

=> $\frac{9x\times r\times25}{100}=5x$

=> $\frac{9r}{4}=5$

=> $x=\frac{5\times4}{9}=\frac{20}{9}\%$

=> Ans – (C)

8) Answer (B)

Principal sum = Rs. 67,400 and simple interest = Rs. 4718

Let rate of interest = $r\%$ and time period = $\frac{14}{12}=\frac{7}{6}$ years

=> Simple interest = $\frac{P\times R\times T}{100}$

=> $\frac{67,400\times r\times7}{6\times100}=4718$

=> $\frac{4718r}{6}=4718$

=> $r=6\%$

=> Ans – (B)

9) Answer (D)

Let sum lent for 24% = Rs. $100x$ and sum lent for 10% = Rs. $(17500-100x)$

Time period = 5 years

=> Simple interest = $\frac{P\times R\times T}{100}$

According to ques,

=> $\frac{100x\times24\times5}{100}+\frac{(17500-100x)\times10\times5}{100}=13300$

=> $120x+(175-x)\times50=13300$

=> $120x+(175\times50)-50x=(175\times76)$

=> $70x=175(76-50)$

=> $x=\frac{175\times26}{70}=65$

$\therefore$ Required ratio = $\frac{100\times65}{17500-(100\times65)}$

= $\frac{6500}{11000}=\frac{65}{110}=13:22$

=> Ans – (D)

10) Answer (C)

Principal sum = Rs. 4000 and time period = 3 years

=> Amount after simple interest = Rs. 5800

Thus, simple interest = Rs. (5800-4000) = Rs. 1800

Let rate of interest = $r\%$

=> Simple interest = $\frac{P\times R\times T}{100}$

=> $\frac{4000\times r\times3}{100}=1800$

=> $120r=1800$

=> $r=\frac{1800}{120}=15\%$

$\therefore$ Amount under compound interest = $P(1+\frac{R}{100})^T$

= $4000(1+\frac{15}{100})^2$

= $4000(1+\frac{3}{20})^2=4000(\frac{23}{20})^2$

= $4000\times\frac{529}{400}$

= $10\times529=Rs.$ $5290$

=> Ans – (C)

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11) Answer (B)

Principal (P) = Rs. 40,000

Rate of interest (r) = 8% and time period (t) = 3 years

Simple interest = $\frac{P \times r \times t}{100}$

= $\frac{40,000 \times 8 \times 3}{100}$

= $400 \times 24=Rs.$ $9600$

Compound interest = $P[(1+\frac{r}{100})^t-1]$

= $40,000[(1+\frac{8}{100})^3-1]$

= $40,000[(\frac{27}{25})^3-1]$

= $40,000 (\frac{19683-15625}{15625})=40,000 \times \frac{4058}{15625}$

= $Rs.$ $10388.48$

$\therefore$ C.I. – S.I. = $10388.48-9600=Rs.$ $788.48$

=> Ans – (B)

12) Answer (C)

Let the given sum = Rs. $100x$

Rate of interest = 5% and time period = 2 years

Compound interest = $P [(1 + \frac{R}{100})^T – 1]$

= $100x [(1 + \frac{5}{100})^2 – 1]$

= $100x [(\frac{21}{20})^2 – 1] = 100x (\frac{441 – 400}{400})$

= $100x \times \frac{41}{400} = 10.25x$

Simple interest = $\frac{P \times R \times T}{100}$

= $\frac{100x \times 5 \times 2}{100} = 10x$

=> Difference between simple and compound interests = $10.25-10x = 41$

=> $0.25x = 41$

=> $x = \frac{41}{0.25} = 164$

$\therefore$ Value of given sum = $100 \times 164 = Rs. 16,400$

13) Answer (C)

Let the given sum = Rs. $1000x$

Rate of interest = 10% and time period = 3 years

Compound interest = $P [(1 + \frac{R}{100})^T – 1]$

= $1000x [(1 + \frac{10}{100})^3 – 1]$

= $1000x [(\frac{11}{10})^3 – 1] = 1000x (\frac{1331 – 1000}{1000})$

= $1000x \times \frac{331}{1000} = 331x$

Simple interest = $\frac{P \times R \times T}{100}$

= $\frac{1000x \times 10 \times 3}{100} = 300x$

=> Difference between simple and compound interests = $331-300x = 93$

=> $31x = 93$

=> $x = \frac{93}{31} = 3$

$\therefore$ Value of given sum = $1000 \times 3 = Rs. 3,000$

14) Answer (C)

Let the sum = Rs. $100x$

For compound interest, rate of interest (r) = 10% and time (t) = 2 years

=> $C.I. = P[(1+\frac{r}{100})^t-1]$

=> $100x[(1+\frac{10}{100})^2-1]=525$

=> $100x[(\frac{11}{10})^2-1]=525$

=> $100x \times (\frac{121-100}{100})=525$

=> $21x=525$

=> $x=\frac{525}{21}=25$

$\therefore$ Sum invested = Rs. 2500

For simple interest, rate of interest (r) = 5% and time (t) = 4 years

=> $S.I.= \frac{P \times r \times t}{100}$

= $\frac{2500 \times 5 \times 4}{100}$

= $25 \times 20=Rs.$ $500$

=> Ans – (C)

15) Answer (C)

Principal (P) = Rs. 64,000

Time (t) = 3 years and rate of interest under compound interest (r) = 7.5%

=> $C.I. = P[(1+\frac{r}{100})^t-1]$

= $64000[(1+\frac{7.5}{100})^3-1]$

= $64000[(1+\frac{15}{200})^3-1]$

= $64000[(\frac{43}{40})^3-1]$

= $64000 \times \frac{(43)^3-(40)^3}{64000}$

= $79507-64000=Rs.$ $15,507$

=> Ans – (C)

16) Answer (C)

17) Answer (C)

Principal amount = Rs. 10,000

Rate of interest = 10% for first year and 12% for second year

=> Amount after interest = $10,000 \times \frac{110}{100} \times \frac{112}{100}$

= $110 \times 112=Rs.$ $12,320$

=> Ans – (C)

18) Answer (B)

Principal (P) = Rs. 6250

Rate of interest (r) = 8% and time period (t) = 2 years

Simple interest = $\frac{P \times r \times t}{100}$

= $\frac{6250 \times 8 \times 2}{100}$

= $62.5 \times 16=Rs.$ $1000$

Compound interest = $P[(1+\frac{r}{100})^t-1]$

= $6250[(1+\frac{8}{100})^2-1]$

= $6250[(\frac{27}{25})^2-1]$

= $6250 \times (\frac{104}{625})$

= $Rs.$ $1040$

$\therefore$ C.I. – S.I. = $1040-1000=Rs.$ $40$

=> Ans – (B)

19) Answer (D)

Principal (P) = Rs. 5000

Rate of interest (r) = 8% and time period (t) = 2 years

Simple interest = $\frac{P \times r \times t}{100}$

= $\frac{5000 \times 8 \times 2}{100}$

= $50 \times 16=Rs.$ $800$

Compound interest = $P[(1+\frac{r}{100})^t-1]$

= $5000[(1+\frac{8}{100})^2-1]$

= $5000[(\frac{27}{25})^2-1]$

= $5000 \times (\frac{104}{625})$

= $Rs.$ $832$

$\therefore$ C.I. – S.I. = $832-800=Rs.$ $32$

=> Ans – (D)

20) Answer (D)

Rate of interest (r) = 4 % and time (t) = 2 years

Difference between simple and compound interests (d) = Rs. 1

Then, the sum = $\frac{d \times (100)^t}{(r)^t}$

= $\frac{1 \times (100)^2}{(4)^2} = \frac{10000}{16}$

= Rs. 625

=> Ans – (D)

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