- Speed, Time and Distance:

Speed = (Distance/ Time), Time= (Distance/Speed), Distance = (Speed x Time).

Time Speed - km/hr to m/sec conversion:

x km/hr = x x 5/18 m/sec. - m/sec to km/hr conversion:

x m/sec = x x 18/5 km/hr.

- If the ratio of the speeds of A and B is a : b, then the ratio of the

the times taken by then to cover the same distance is

1/a : 1/b or b : a. - Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,

the average speed during the whole journey is

(2xy/ x + y) km/hr.

## Compound Interest

Let Principal = P, Rate = R% per annum, Time = n years.

When interest is compound Annually:

Amount = P (1 + R/100) n

When interest is compounded Half-yearly:

Amount = P [1 + (R/2)/100] 2n

When interest is compounded Quarterly:

Amount = P [1 + (R/4)/100] 4n

When interest is compounded Annually but time is in fraction, say 3 years.

Amount = P [1 + R/100]3 x (1+ 2/5r/100)

When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Then, Amount = P (1 +r1/100)(r2/100)(1+r3/100)

Present worth of Rs. x due n years hence is given by:

Present Worth x=/(1+r/100)

### MCQS:

A** bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1stJanuary and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:**

A. Rs. 120

B. Rs. 121

C. Rs. 122

D. Rs. 123

**Answer: Option B**

Explanation:

Amount = Rs. [1600 x (1 +5/2+100)2 +1600 x (1+5/2+100)

Rs [1600 x 41/40 x 41/40+1600 x 41/40] Rs [1600 x 41/40 (41/40 + 1)] Rs [1600 x 41 x 81/40 x 40] Rs. 3321 C.I = Rs. (3321-3200) Rs=121

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

A. 625

B. 630

C. 640

D. 650

**Answer: Option A**

Explanation:

Let the sum be Rs. x. Then,

C.I. = [x (1 + 4/100)2-x]=[676/ 625 x-x]=51/625 x

S.I. = (x x 4 x 2/100) = 2x/25 51x/625 – 2x/25 = 1

x=625

**There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?**

A. Rs. 2160

B. Rs. 3120

C. Rs. 3972

D. Rs. 6240

E. None of these

**Answer: Option C**

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R = (100 x 60/100 x 6) = 10% p.a.

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I. = [Rs. 12000 x {(1 +10/100)3 – 1}]

= Rs. (12000 x 331/1000)

= 3972

**What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?**

A. Rs. 2.04

B. Rs. 3.06

C. Rs. 4.80

D. Rs. 8.30

**Answer: Option A**

Explanation:

C.I. when interest

compounded yearly

= Rs. 5000 x (1 + 4/100) x (1 + 1/2 x 4/100)]

= Rs. 5000 x 26/25 x 51/50

= Rs. 5304.

C.I. when interest is

compounded half-yearly

= Rs. [5000 x (1 + 2/100)3]

= Rs. (5000 x 51/50 x 51/50 x 51/50)

= Rs. 5306.04

Difference = Rs. (5306.04 – 5304) = Rs. 2.04

**The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:**

A. 2

B. 2 1/2

C. 3

D. 4

**Answer: Option A**

Explanation:

Amount = Rs. (30000 + 4347) = Rs. 34347. Let the time be *n *years. Then, 30000 (1 + 7/100)n = 34347 (107/100) = 34347/30000 = 11449/10000 = (107/100)2

n = 2 years.

**What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?**

A. Rs. 9000.30

B. Rs. 9720

C. Rs. 10123.20

D. Rs. 10483.20

E. None of these

**Answer: Option C**

Explanation:

Amount = Rs. [25000 x (1 + 12/100)3]

= Rs. (25000 x 28/25 x 28/25 x 28/25

= Rs. 35123.20

C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20

**At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?**

A. 6%

B. 6.5%

C. 7%

D. 7.5%** Answer: Option A**

Explanation:

Let the rate be R% p.a.

Then, 1200 x (1 + R/100)2 = 1348.32

(1+R/100)2 = 134832/120000 =11236/10000

(1 + R/100)2 = (106/100)2 1+ R/100 = 106/100

R = 6%

**The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:**

A. 3

B. 4

C. 5

D. 6

**Answer: Option B**

Explanation:

P (1 + 20/100)n > 2P => (6/5)n > 2

Now, (6/5 x 6/5 x 6/5 x 6/5)>2

So, n = 4 years.

**Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?**

A. Rs. 8600

B. Rs. 8620

C. Rs. 8820

D. None of these

**Answer: Option C**

Explanation:

Amount = Rs. [8000 x (1 + 5/100)2]

= Rs. (8000 x 21/20 x 21/20

= Rs. 8820.

**The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:**

A. 6.06%

B. 6.07%

C. 6.08%

D. 6.09%

**Answer: Option D**

Explanation:

Amount of Rs. 100 for 1 year

when compounded half-yearly

= Rs. [100 x (1 + 3/100)2] = Rs. 106.09

Effective rate = (106.09 – 100)% = 6.09%

**Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:**

A. Rs. 1550

B. Rs. 1650

C. Rs. 1750

D. Rs. 2000

** Answer: Option C**

Explanation:

C.I. = Rs. [4000 x (1 + 10/100)2 – 4000]

= Rs. (4000 x 11/10 x 11/10 – 4000)

= Rs. 840.

Sum = Rs.(420 x 100/3 x 8) = Rs. 1750.

**If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?**

A. Rs. 51.25

B. Rs. 52

C. Rs. 54.25

D. Rs. 60

** Answer: Option A**

Explanation:

Sum = Rs.(50 x 100/2 x 5)= Rs. 500.

Amount = Rs. [500 x (1 + 5/100)2]

= Rs. 500 x 21/20 x 21/20

= Rs. 551.25

C.I. = Rs. (551.25 – 500) = Rs. 51.25

**The difference between simple interest and compound on Rs. 1200 for one year at 10% per annul reckoned half-yearly is:**

A. Rs. 2.50

B. Rs. 3

C. Rs. 3.75

D. Rs. 4

E. None of these

**Answer: Option B**

Explanation:

S.I. = Rs

1200 x 10 x 1/100 = Rs. 120.

C.I. = Rs. [1200 x (1 + 5/100)2 – 1200 = Rs. 123.

Difference = Rs. (123 – 120) = Rs. 3.

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

A. 8

B. 10

C. 12

D. Cannot be determined

E. None of these

**Answer: Option A**

Explanation:

[15000 x (1 + R/100)2 – 15000 -] – (15000 x R x 2/100) = 96

15000 [(1 + R/100)2-1 – 2R/100] = 96

15000 [(100 + R)2 – 10000 – (200 x R)/10000] = 96

R2 = (96 x 2/3) = 64

R = 8.

Rate = 8%.

**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. 400

B. Rs. 500

C. Rs. 600

D. Rs. 800

**Answer: Option B**

Explanation:

Let the sum be Rs. P.

Then, [P (1 + 10/100)2 – P] = 525

P [(11/10)2 -1] = 525

P =( 525 x 100/21) = 2500.

Sum = Rs . 2500.

So, S.I. = Rs. (2500 x 5 x 4/100)

= Rs. 500

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