**Interest:**The money paid by the borrower to the lender for the use of money is called Interest.

**Principal:**The sum lent is called principal.

**Simple Interest =**

PTR
100

Where
P = Principal R= Rate of interest per annum

T=
Time period in years

**Amount**= Principal + Simple Interest

Amount=>
A = P x $\frac{100+RT}{2}$

**Solved Problems on Simple Interest:**

**1**. Find the simple interest on Rs 8000 for 4 years at 10% p.a rate of interest?

a)
Rs 3500 b)Rs 4000 c)Rs 2400 d)Rs
4800

**Answer : B**

**Explanation :**Simple Interest =

PTR
100

= 8000 X 5 X

10
100

= Rs 4000**2**. Find the simple interest on Rs 2400 for 8 years 4 months at 6% per annum rate of interest ?

a)Rs 750 b)Rs
800 c)Rs 600 d)Rs 1200

**Answer : D**

**Explanation:**

Time period is 8 years 4 months = 8

4
12

years =
25
3

years
Simple Interest =

PTR
100

= 2400 x
25
3

x
6
100

=Rs
1200**3**. What is the simple interest on Rs 8000 from August 6

^{th}to December 30

^{th}at 5% p.a rate of interest?

a)Rs 240 b)Rs
200 c)Rs 160 d)Rs 120

**Answer: C**

**Explanation:**Number of days from August 6

^{th}to December 30

^{th}= 146 days ( we don’t count the given day)

Simple
Interest=

PTR
100

= 8000 x
146
365

x
5
100

= Rs 160

**4**. What is the simple interest on Rs 2400 for 9 months at 4 paisa per rupee per month?

a)Rs 864 B)Rs
800 c)Rs 432 d)Rs 216

**Answer: A**

**Explanation:**P = Rs 2400

Time Period T = 9 months =

9
12

years = ¾ year
Rate of
interest =4 paisa per Rupee per month= 4% per month= 48% p.a

Simple Interest=

PTR
100

= 2400 X $\frac{3}{4}$
X
48
100

= Rs 864**5**. At what rate of interest per annum, will Rs 5500 be obtained as simple interest on Rs 25000 for 2 years 9 months?

a)
10% b)9% c)8% d)7%

**Answer :**

**Explanation:**Given P= Rs 25000 and

Time period = 2 years 9 months= 2

9
12

=
11
4

years
Simple
Interest=

PTR
100

5500 = 25000 X

11
4

X
R
100

R = 8 %

**6**. A man borrowed Rs 10000 from a lender at 9% per annum rate of interest .Find the amount to be paid by the man after 2 years 6 months?

a)
Rs 12000 b)Rs 12500 c)Rs 12250 d)Rs 15000

**Answer :C**

**Explanation:**

Principal
= Rs 10000 Rate of interest R =
9%

T=
2 years 6 months= 2 ½ years=

5
2

years
Simple
Interest=

PTR
100

= 10000 X
5
2

X
9
100

= Rs 2250
Amount= Prinipal + Simple interest = Rs
10000+ Rs 2250 = Rs 12250

**To find simple interest, we have a direct formula**

*Alternate Method:*
A= P

(100+RT)
100

= 10000 $ \frac{100+\frac{5}{2}\times9}{100}$

= Rs 12250

**7.**Sharma deposited Rs 9000 in a financial institution at 8% per annum rate of interest for 3 years. For many years must Tripathi deposit Rs 5,400 at 10% per annum rate of interest in another financial institution, so that both of them get same simple interest?

a)
4 years b)10 years c)12 years d)14 years

**Answer: A**

**Explanation:**The simple interest on Rs 9000 at 8% rate of interest for 3 years should be equal to the simple interest on Rs 5400 at 10% for unknown years.

9000 X 3 X

8
100

= 5400 X T
x
10
100

Therefore T = 4 years

Tripathi
should deposit for 4 years to get same interest as Sharma

**8.**

**Mr Bhattacharyya lent Rs 3600 to Mr Tiwary for 3 years and Rs 6600 to Mr Mishra for 2 years and he received Rs 1200 as simple interest in all. Find the rate of interest per annum?**

a)
4% b)5% c)6% d)12%

**Answer: B**

**Explanation:**

SI on 3600 for 3 years + SI on Rs 6600 for 2 years = 1200

3600 x 3 x

R
100

+ 6600 x 2 x
R
100

= 1200
Ã° 108R
+132R = 1200

Ã° 240R=
1200

Ã° R=
5%

The
rate of interest per annum is 5%

**9.**The simple interest on a sum of money is $ \frac{1}{25}$ th of the principal. If the rate of interest is 16%. Find the time period?

a)
1 month b)2 months c)3 months d)4 months

**Answer: C**

**Explanation**: Simple interest is

1
25

of the principal => SI =
1
25

P
1
25

P= P
x
16
100

x T=>T= $\frac{1}{4}$
years
Therefore, the time period is

1
4

^{th}year = 3 months**10.**The simple interest on a sum of money is $\frac{4}{25}$ of the principal and the rate of interest is equal to the number of years . What is the rate of interest?

a)4% b)8% c)16% d)18%

**Answer : A**

**Explanation :**

Simple interest is

4
25

^{th}of the principal => SI =

4
25

P.Rate of interest per annum is equal to number of years => R =T

SI =

PTR
100

4
25

P = P X R X
R
100

=>R

^{2}=
400
25

=>R=
20
5

=4%**11**

**.**A sum was put at a simple interest at a certain rate of 4 years. Had it been put a 3% higher rate, it would have fetched Rs 720 more. Find the principal?

a)Rs 4500 b)Rs 5000 c)Rs 6000 d)Rs
7200

**Answer:C**

**Explanation:**Let rate of interest be R and principal be P.

SI at R rate of interest=> SI = P X 4 x

(R+4)
25

If the rate of interest is 4% more, then SI= P X 4 x
(R+4)
25

The difference between these two simple interests is Rs
720

P X 4 x

(R+4)
25

- P X 4 x
(R+4)
25

= 720
P X
4 X

4
25

= 960
Therefore P= Rs 6000

**12.**Mr Shastri invested certain sum of money at 7% p.a for 4 years. However he would get Rs 1040 more simple interest, if he invests the same sum of money at 6% for 9 years. Find the sum (principal)?

a)Rs 8000 b)Rs 6000 c)Rs 5000 d)Rs 4000

**Answer: D**

**Explanation:**The difference between the simple interest obtained in two cases is Rs 1040.

Let
Principal be P .

(P X 9 X

6
100

) - (P X 4 X
7
100

) = 1040
Ã° $\frac{54P}{100}$
- $\frac{26P}{100}$
= 1040

Ã° $\frac{26P}{100}$
=
Rs 1040

Ã° P=Rs 4000

**13**In how many years will a sum of money becomes 4 times at 5% p.a simple interest?

a) 40 years b)50 years c)60 years d)25 years

**Answer:C**

**Explanation:**Sum of money becomes 4 times=> Amount= 4P

Amount= P+ SI =>Simple
interest= 4P-P

SI = P T

R
100

=> 3P= P X T X
5
100

Ã° T=
60 years

**14.**A sum of money becomes 4 times in 9 years at simple interest. In how many years will it become 8 times of itself at the same rate?

a)
21 years b)18 years c)15 years d)12 years

**Answer:A**

**Explanation**:A sum of money ( principal) P becomes 4 times => Amount= 4P

Simple interest obtained is 3P

To get simple interest 3P, it takes 9 years.

To get simple interest P, it takes

9
3

= 3 years
Now it has to
become 8 times => The simple interest to be obtained is 7P

To get simple
interest P, it take s 3 years

So to get 7P as simple interest, it takes 7 x 3 = 21 years

**15.**Mr Gupta purchased an Apple mobile, He paid 12000 in cash and promised to pay Rs 40,320 after 3 years. If the rate of interest is 4% p.a, what is the price of the Mobile at present?

a)Rs 40000 b)Rs 48000 c)Rs
50000 d)Rs 52000

**Answer:B**

**Explanation:**Rs 40,320 to be paid after 3 years is equal to P present.

Amount = P

(100+RT)
100

Ã° 40320=
P x

(100+ 3 X 4)
100

Ã° P=
40320 x $\frac{100}{112}$
= Rs 36000

Price
of the mobile at present= Rs 36000+ Rs 12000 = Rs 48000

**16.**A certain sum of money amounts to Rs 2400 in 3 years and Rs 2720 in 5 years. Find the principal?

a)
Rs 1920 b)Rs 2050 c)Rs 2140 d)Rs
2250

**Answer:A**

**Explanation:**We know that Amount= Principal + Simple Interest

Principal + SI for 5 years= Rs 2720 (i)

Prinipical + SI for 3 years= Rs 2400 --(ii)

(i)-(ii)
gives the SI for 2 years = 320

Simple interest for one year = Rs

320
2

=
160
Given
P+SI for 3 years= 2400

Ã° P
+ 3 x 160 = 2400 =>P=2400-480=Rs 1920

**17.**A sum of money Rs 32000 is lent in two parts, one at the rate of 10% and another at 12% . If the annual interest received is Rs 3600. What is the amount lent at 12%?

a)Rs 15000 b)Rs 18000 c)Rs
20000 d)Rs 24000

**Answer:C**

**Explanation:**Let P be the money lent at 10% .

Then
(32000- P) is lent at 12%

Simple
interest on both amounts is equal to Rs 3600

P X
1 X

10
100

+ (32000-P) X 1 X
12
100

= 3600
Ã° $\frac{10P}{100}$
+ 32000X $\frac{12}{100}$ – $\frac{12P}{100}$= 3600

Ã° $\frac{2P}{100}$
= 3840-3600

Ã° 2P=
240 X 100 =>P =Rs 12000

Money lent at 12%= (32000-12000)= 20000.

Money lent at 12%= (32000-12000)= 20000.