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Formulas,

shortcuts, tricks and solved examples:

If P =

Principal, A = Amount, R = Rate percent per year, T = T years, S.I = Simple

interest, C.I = Compound interest, Then,

Principal, A = Amount, R = Rate percent per year, T = T years, S.I = Simple

interest, C.I = Compound interest, Then,

**1. For Simple interest:**

(A). S.I =

(P × R × T)/100

(P × R × T)/100

(B) A = P +

S.I

S.I

**2. For Compound interest:**

(A) When

interest is compounded yearly,

interest is compounded yearly,

(B) When

interest is compounded half-yearly,

interest is compounded half-yearly,

(C) When

interest is compounded quarterly

(D) When

time is in fraction of a year, say 2⅕

(E) If rate

of interest in 1st year, 2nd year …………..… nth year are R1%, R2%

…………. Rn% respectively, then,

**3. Equivalent or Successive interest:**

Single

equivalent interest rate or Successive interest rate of 20% and 10% is

equivalent interest rate or Successive interest rate of 20% and 10% is

Single

equivalent interest rate or Successive interest rate of 10%, 20% and 30% would

be

equivalent interest rate or Successive interest rate of 10%, 20% and 30% would

be

Since,

equivalent interest 10% and 20% is 28%

equivalent interest 10% and 20% is 28%

So,

equivalent interest of 28% and 30% will be,

equivalent interest of 28% and 30% will be,

__Example: 01__

**A sum of Rs. 15,500 is lent out into two**

parts, one at 8% and another one at 6%. If the total annual income is Rs. 1060,

the money lent at 8% is:

parts, one at 8% and another one at 6%. If the total annual income is Rs. 1060,

the money lent at 8% is:

__Solution:__
Let the

money lent at 8% be Rs. x, then

money lent at 8% be Rs. x, then

[(x × 8 ×

1)/100] + [15500 – x) × 6 × 1/100] = 1060

1)/100] + [15500 – x) × 6 × 1/100] = 1060

or, 2x +

93000 = 106000

93000 = 106000

or, x = 6500

Therefore, the

money lent at 8% is Rs. 6500

money lent at 8% is Rs. 6500

__Example: 02__**A sum of money at compound interest amounts**

to Rs. 10,580 in 2 years and to Rs. 12,176 in 3 years. The rate of interest per

annum is:

to Rs. 10,580 in 2 years and to Rs. 12,176 in 3 years. The rate of interest per

annum is:

__Solution:__
Interest on

Rs. 10580 for 1 year = Rs. (12176 – 10580) = Rs. 1587

Rs. 10580 for 1 year = Rs. (12176 – 10580) = Rs. 1587

∴ Rate = [(100 × 1587)/10580]% = 15%

Hence, the

rate of interest per annum is 15%.

rate of interest per annum is 15%.

__Example: 03__**A sum of money becomes Rs. 13,380 after**

3 years and Rs. 20,070 after 6 years on compound interest. The sum is:

3 years and Rs. 20,070 after 6 years on compound interest. The sum is:

__Solution:__
Let, the sum

be x, then

be x, then

x[1 + (R/100)]3 =

13380 and, x[1 + (R/100)]6 = 20070

13380 and, x[1 + (R/100)]6 = 20070

On dividing,

we get, [1 + (R/100)]3 = (20070/13380) = 3/2

we get, [1 + (R/100)]3 = (20070/13380) = 3/2

∴ x (3/2) = 13380

or, x = 13380 × (3/2)

= 8920

= 8920

Hence, the

sum is Rs. 8920.

**SOLVE EXAMPLE **

__Question No. 01__**A sum**

fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5

years. What is the sum?

fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5

years. What is the sum?

(A) Rs.

4462.50

4462.50

(B) Rs.

8032.50

8032.50

(C) Rs. 8900

(D) Rs. 8925

Answer:

Option D

Option D

__Explanation:__
Principal =

Rs. (100 × 4016.25)/(9 × 5)

Rs. (100 × 4016.25)/(9 × 5)

= Rs. (401625/45) = Rs. 8925.

__Question No. 02__**Calculate**

the amount on Rs. 4480 at 8% per annum for 3 years.

the amount on Rs. 4480 at 8% per annum for 3 years.

(A) Rs.

5555.20

5555.20

(B) Rs. 5545.20

(C) Rs. 5000

(D) Rs. 6555

Answer:

Option A

Option A

__Explanation____:__

S.I. = (P × N

× R)/100

× R)/100

= Rs. (4480 × 3 × 8)/100

= Rs. 1075.20

∴ Amount

= Rs. (4480 + 1075.20)

= Rs. (4480 + 1075.20)

= Rs. 5555.20

__Question No. 03__**A certain**

sum of money at simple interest amounts to Rs. 1260 in 2 years and to Rs. 1350

in 5 years. The rate percent per annum is?

sum of money at simple interest amounts to Rs. 1260 in 2 years and to Rs. 1350

in 5 years. The rate percent per annum is?

(A) 35 %

(B) 25 %

(C) 50 %

(D) 45 %

Answer:

Option B

Option B

__Explanation____:__

S.I. for 3

years = Rs. (1350 – 1260) = Rs. 90

years = Rs. (1350 – 1260) = Rs. 90

∴ S.I.

for 2 years = Rs. (90/3) × 2 = Rs. 60

for 2 years = Rs. (90/3) × 2 = Rs. 60

Principal =

Rs. (1260 – 60) = Rs. 1200

Rs. (1260 – 60) = Rs. 1200

Rate, R = (100

× 60)/(1200 × 2) % = 25 %

× 60)/(1200 × 2) % = 25 %

__Question No. 04__**Mr. Roy**

invested an amount of Rs. 13,900 divided in two different schemes A and B at

the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total

amount of simple interest earned in 2 years be Rs. 3508, what was the amount

invested in Scheme B?

invested an amount of Rs. 13,900 divided in two different schemes A and B at

the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total

amount of simple interest earned in 2 years be Rs. 3508, what was the amount

invested in Scheme B?

(A) Rs. 6400

(B) Rs. 6500

(C) Rs. 7200

(D) Rs. 7500

Answer:

Option A

Option A

__Explanation:__
Let the sum

invested in Scheme A be Rs.

(13900 –

invested in Scheme A be Rs.

*x*and that in Scheme B be Rs.(13900 –

*x*).
Then, [

14 × 2)/100] + [{(13900 –

*x*×14 × 2)/100] + [{(13900 –

*x*) × 11 × 2}/100] = 3508
=> 28

22

*x*–22

*x*= 350800 – (13900 × 22)
=> 6

45000

*x*=45000

=> x =

7500.

7500.

So, sum

invested in Scheme B = Rs. (13900 – 7500) = Rs. 6400.

invested in Scheme B = Rs. (13900 – 7500) = Rs. 6400.

__Question No. 05__**How much**

time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5%

per annum of simple interest?

time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5%

per annum of simple interest?

(A) 3.5

years

years

(B) 4 years

(C) 4.5

years

years

(D) 5 years

Answer:

Option B

Option B

__Explanation:__
Time = [(100

× 81)/( 450 × 4.5)] years = 4 years.

× 81)/( 450 × 4.5)] years = 4 years.

__Question No. 06__**A sum of Rs.**

725 is lent in the beginning of a year at a certain rate of interest. After 8

months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At

the end of the year, Rs. 33.50 is earned as interest from both the loans. What

was the original rate of interest?

725 is lent in the beginning of a year at a certain rate of interest. After 8

months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At

the end of the year, Rs. 33.50 is earned as interest from both the loans. What

was the original rate of interest?

(A) 3.6%

(B) 4.5%

(C) 5%

(D) None of

these

these

Answer:

Option D

Option D

__Explanation:__
Let the

original rate be R%. Then, new rate = (2R)%.

original rate be R%. Then, new rate = (2R)%.

Here,

original rate is for 1 year(s); the new rate is for only 4 months i.e. for 1/3

year.

original rate is for 1 year(s); the new rate is for only 4 months i.e. for 1/3

year.

∴

[(725 × R × 1)/100] + [362.50 × 2R × 1)/(100 × 3)] = 33.50

[(725 × R × 1)/100] + [362.50 × 2R × 1)/(100 × 3)] = 33.50

=> (2175

+ 725) R = 33.50 × 100 × 3

+ 725) R = 33.50 × 100 × 3

=> (2175

+ 725) R = 10050

+ 725) R = 10050

=> (2900)

R = 10050

R = 10050

=> R = (10050/2900)

= 3.46

= 3.46

∴ Original

rate = 3.46%

rate = 3.46%

__Question No. 07__**A certain**

amount earns simple interest of Rs. 1750 after 7 years. Had the interest been

2% more, how much more interest would it have earned?

amount earns simple interest of Rs. 1750 after 7 years. Had the interest been

2% more, how much more interest would it have earned?

(A) Rs. 35

(B) Rs. 245

(C) Rs. 350

(D) Cannot be

determined

determined

Answer:

Option D

Option D

__Explanation:__
We need to

know the S.I., principal and time to find the rate.

know the S.I., principal and time to find the rate.

Since the

principal is not given, so data is inadequate.

principal is not given, so data is inadequate.

__Question No. 08__**Ravi took**

a loan of Rs. 1200 with simple interest for as many years as the rate of

interest. If she paid Rs. 432 as interest at the end of the loan period, what

was the rate of interest?

a loan of Rs. 1200 with simple interest for as many years as the rate of

interest. If she paid Rs. 432 as interest at the end of the loan period, what

was the rate of interest?

(A) 3.6

(B) 6

(C) 18

(D) None of

these

these

Answer:

Option B

Option B

__Explanation:__
Let rate =

R% and time = R years.

R% and time = R years.

Then, (1200 ×

R × R)/100 = 432

R × R)/100 = 432

=> 12R2 =

432

432

=> R2 =

36

36

=> R = 6.

__Question No. 09__**S.I. on Rs.**

1500 at 7% per annum for a certain time is Rs. 210. Find the time;

1500 at 7% per annum for a certain time is Rs. 210. Find the time;

(A) 3 years

(B) 5 years

(C) 2 years

(D) 1½ years

Answer:

Option C

Option C

__Explanation____:__

Time, N = (210

× 100)/(1500 × 7) = 2 years

× 100)/(1500 × 7) = 2 years

__Question No. 10__**A sum of**

money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4

years. The sum is:

money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4

years. The sum is:

(A) Rs. 650

(B) Rs. 690

(C) Rs. 698

(D) Rs. 700

Answer:

Option C

Option C

__Explanation:__
S.I. for 1

year = Rs. (854 – 815) = Rs. 39.

year = Rs. (854 – 815) = Rs. 39.

S.I. for 3

years = Rs. (39 × 3) = Rs. 117.

years = Rs. (39 × 3) = Rs. 117.

∴ Principal

= Rs. (815 – 117) = Rs. 698

= Rs. (815 – 117) = Rs. 698