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**. As I promised yesterday, here is the Day 1 class of our SBI Clerks 2018 Classes. As we have less time, I don't want to waste much time on useless topics. So I am directly starting one of the most important and difficult topic of Aptitude section,**

*Aparna***Simple Interest**. In banking exams, you will get at-least one question from

*. I will try my best to explain everything in details and will help you solve SI problems on your own.*

__Simple Interest / Compound Interest__## Simple Interest Shortcuts

**Basics - Simple Interest Introduction**

**What is Interest ?**

Suppose you badly need Rs. 100/- to buy something. But you don't have that money. So you will ask your friends or somebody else (Say Mr. X) for that money. But why should Mr. X give you the money ? What advantage will he get by giving you the money ?

So, to convince him, you will say that you will return his Rs. 100/- in one or two years and promise him that you will pay some additional amount for the usage of his money.

Then he gives you the money and will asks you to pay additional Two rupees per year for using his money.

You agree for this arrangement (because you badly in need of that Rs. 100/-) and take the money.

After two years, you got a Rs.100/- from somewhere and wanted to return the money of Mr. X. So now you need to pay his 100 along with the additional money you promised (Rs. 2 per year) for keeping his Rs. 100/- with you. That means, you should pay additional Rs. 4 (2+2) for two years. This additional money is called as

**Interest**. If the interest is calculated on same amount of money, it is called the

*. The*

**Simple Interest***.*

__Simple Interest will be the same for all the years__
But some times Mr. X asks you to give interest for the additional amount too. That means, by the end of the 1st year, you will have to pay Mr. X

**Rs. 102**(100 + 2 rupees interest). So from the second year onwards, Mr. X will ask you to pay interest for this Rs. 102 instead of Rs. 100. This interest is called as Compound Interest.**Definitions**:

The amount charged by the lender for giving you his money for a specific amount of time.*Simple Interest*:Here also same. But here the lender calculates the Interest on Interest if the given time exceeds*Compound Interest*:

We shall discuss about Compound Interest in tomorrow's lesson. Now let's work with Simple Interest.

**Note : Please keep a Note Books for the practice purpose. Trust me, merely reading this lesson won't help you in any way. You need to practice on your own to be expert in Simple Interest problems.**###
__Simple Interest Formulas__

__Simple Interest Formulas__

**1.**

**SI = PTR / 100**

Here,

**SI**= Simple Interest

**P**= Principal

**T**= Time in years

R = Rate % per annum

2.

**P = 100I / TR**

3.

**T = 100I / PR**

4.

**R = 100I / PT**

5.

**A = P + I**, where A = Amount

6.

**P = 100A / (100 + TR)**

7. If a sum of money becomes

*x*times in T years at R % p.a (per anum), then

**TR = 100 (**or

*x*-1)**TR = 100**

*x*- 1008. If a sum of money becomes n times in t years and N times in T years, then

**t / T = (n-1) / (N-1)**

9. If the interest is the same in two cases, then

**p t r = P T R**

10. If the principal is the same in two cases, then

**i / tr = I / TR**

11. If the time is the same in two cases, then

**i / pr = I / PR**

12. If the rate is the same in two cases, then

**i / pt = I / PT**

13. If a sum is put at R % p.a higher rate and the additional interest fetched is

**Rs. I**, then sum =

**P = 100I / TR**

14. If a sum amounts to Rs. X in T years and Rs. Y in t years, then the interest for one year

**= I 1 = (X~Y) / (T~t), Sum = P = X-I1T or Y-I1t and Rate % pa = (100I1) / P**

15. If the interests are the same in some cases, the ratio of the sums is same as the ratio of the values of the reciprocals of

**T x R.**

16. If the amounts are the same in some cases, the ratio of the sums is same as the ratio of the values of the reciprocals of

**(100 + T x R)**

Now let's start working on Simple Interest problems.

###
__Simple Interest : Examples & Practice Problems__

**:**

__Model 1__**Find the Simple Interest on Rs. 7500 in 4 years at 15% per annum ?**- Rs. 3000
- Rs. 3600
- Rs. 4500
- Rs. 4800
- None of these

**Solution :**

Here, Principal : Rs. 7500

Time = 4 Years

Rate = 15%

So I = PTR / 100

=> (7500 x 4 x 15) / 100

**Tip**: When ever you see zeros in denominator and numerator which are ready to be cancelled, simply avoid writing them. It will save time.

Here 75 x 4 x 15 = 75x60 = 4500 (Option 3 is the answer).

Now I am sharing 3 problems which are exactly same as above problem (only numbers different) for your practice. Solve them and share your answers in comments section.

**Practice Problems on Model 1**

**Find the Simple Interest on Rs. 7560 in 5 years at 12% per annum ?**- Rs. 4000
- Rs. 4200
- Rs. 4500
- Rs. 4536
- None of these
**Find the Simple Interest on Rs. 7500 in 3 years at 16% per annum ?**- Rs. 3000
- Rs. 3600
- Rs. 45000
- Rs. 4800
- None of these
**Find the Simple Interest on Rs. 17500 in 6 years at 7% per annum ?**- Rs. 7350
- Rs. 7750
- Rs. 7800
- Rs. 8275
- None of these

__:__

**Model 2****On what sum of money will the Simple Interest be Rs. 2000 in 5 years at 8% per annum ?**- Rs. 4000
- Rs. 4500
- Rs. 4800
- Rs. 5000
- None of these

**Solution :**

Here, they are asking for P

So, P = 100I / TR = (100 x 2000) / 40 = 5000

**Practice Problems on Model 2**

**On what sum of money will the Simple Interest be Rs. 1440 in 4 years at 7.5% per annum ?**- Rs. 4000
- Rs. 4500
- Rs. 4800
- Rs. 5000
- None of these
**On what sum of money will the Simple Interest be Rs. 2160 in 6 years at 8% per annum ?**- Rs. 4000
- Rs. 4500
- Rs. 4800
- Rs. 5000
- None of these
**On what sum of money will the Simple Interest be Rs. 3600 in 2 years at 12% per annum ?**- Rs. 15000
- Rs. 14500
- Rs. 16000
- Rs. 20000
- None of these

__:__

**Model 3****A man invested Rs. 20,000 at 10% p.a., Rs. 15,000 at 12% p.a., and some money at 15% p.a., If the total annual interest received is Rs. 5,600, find the money invested by him at 15% p.a.**- Rs. 10000
- Rs. 12000
- Rs. 12500
- Rs. 18000
- None of these

**Solution :**

Here, the total Interest he received is Rs. 56,00.

So, find the total interest and equate it with 56,00

So, the total interest = Σ [ (PTR)/100 ] [ here Sigma symbol ( Σ ) represents the Total]

= 200x10+150x12+ (P/100)x15 = 5600

3800+ (3P/20) = 5600

= 3P/20 = 1800 => P = 12000/-

So, find the total interest and equate it with 56,00

So, the total interest = Σ [ (PTR)/100 ] [ here Sigma symbol ( Σ ) represents the Total]

= 200x10+150x12+ (P/100)x15 = 5600

3800+ (3P/20) = 5600

= 3P/20 = 1800 => P = 12000/-

**Practice Problems on Model 3 :**

**A man invested Rs. 10,000 at 10% p.a., Rs. 12000 at 12% p.a. and some money at 15% p.a. If the total annual interest received is Rs. 4,690, find the money invested by him at 15% p.a.**- Rs. 10000
- Rs. 12000
- Rs. 12500
- Rs. 18000
- None of these
**A man invested Rs. 20,000 at 10% p.a., Rs. 15,000 at 18% p.a. and some money at 15% p.a. If the total biannual interest received is Rs. 14,800 find the money invested by him at 15% p.a. [Note : Here biannual means Two Years]**- Rs. 10000
- Rs. 12000
- Rs. 12500
- Rs. 18000
- None of these
**A man invested Rs. 30,000 at 10% p.a.., Rs. 25,000 at 12% p.a., and some money at 8% p.a., If the total interest received in 3 years is Rs. 21,000 find the money invested by him at 15% p.a.**- Rs. 10000
- Rs. 12000
- Rs. 12500
- Rs. 18000
- None of these

**:**

__Model 4__**On a sum of money the rate of interest is 5% p.a. for the first 3 years, 6% p.a. for the next 4 years and 8% p.a for the next years beyond the first 7 years. If the interest obtained in 12 years is Rs. 3,950, find the sum (or) principle [both are same].**- Rs. 5000
- Rs. 6000
- Rs. 7200
- Rs. 8000
- None of these

**Solution :**

(5% x 3) + (6% x 4) + (8% x 5)

15% + 24% + 40% = 79%

=> 79/100P = 3950

=> P = 395000 / 79 = 5000

**Practice Problems on Model 4**

**On a sum of money the rate of interest is 4% p.a. for the first 3 years, 5% p.a for the next 3 years and 8% p.a for the next years beyond the first 7 years. If the interest obtained in 9 years is Rs. 2,640, find the sum.**- Rs. 5000
- Rs. 6000
- Rs. 7200
- Rs. 8000
- None of these
**On a sum of money the rate of interest is 6% p.a. for the first 2 years, 7% p.a .for the next 3 years and 8% p.a for the next years beyond the first 5 years. If the interest obtained in 8 years is Rs. 4,560, find the sum.**- Rs. 5000
- Rs. 6000
- Rs. 7200
- Rs. 8000
- None of these
**On a sum of money the rate of interest is 5% p.a. for the first 4 years, 6% p.a. for the next 5 years, and 8% p.a. for the next years beyond the first 9 years. If the interest obtained in 12 years is Rs. 5328, find the sum.**- Rs. 5000
- Rs. 6000
- Rs. 7200
- Rs. 8000
- None of these

__:__

**Model 5**

**A sum was put at S.I at a certain rate for 5 years. Had it been put at 3% p.a. higher rate, it would have fetched Rs. 900 more. Find the sum.**- Rs. 4000
- Rs. 4500
- Rs. 5000
- Rs. 5400
- None of these

**Solution :**

Don't be confused. Here the Sum / Principle remains same. Call it as P.

They are saying, if it put for some additional rate, it would have fetched some Additional interest. We already know the formula for finding P.

Find out,

P = 100I / TR [Here I is Additional Interest and R is additional Rate]

= (100x900) / (5x3) = 6000

**Practice Problems on Model 5**

**A sum was put at S.I at a certain rate for 5 years. Had it been put at 4% p.a. higher rate, it would have fetched Rs. 900 more. Find the sum.**- Rs. 4000
- Rs. 4500
- Rs. 5000
- Rs. 5400
- None of these
**A sum was put at S. I at a certain rate for 4 years. Had it been put at 3% p.a. higher rate, it would have fetched Rs. 900 more. Find the sum.**- Rs. 4000
- Rs. 4500
- Rs. 5000
- Rs. 54000
- None of these
**A sum was put at S.I. at a certain rate for 3 years. Had it been put at 6% p.a. higher rate, it would have fetched Rs. 900 more. Find the sum.**- Rs. 4000
- Rs. 4500
- Rs. 500
- Rs. 5400
- None of these

__:__

**Model 6****On a certain sum of money the Simple Interest in 2 years at 10% p.a. is Rs. 125. What would be the Simple Interest if the rate of interest will be 12% p.a. in three years ?**- Rs. 216
- Rs. 225
- Rs. 240
- Rs. 250
- None of these

**Solution :**

Here the Principle is same for both the cases. That means p = P

=> 100i / tr = 100I / TR

= 125 / (2 x 10) = I / (3 x 12)

= > I = 225

= 125 / (2 x 10) = I / (3 x 12)

= > I = 225

**Practice Problems on Model 6 :**

**On a certain sum of money the simple interest in 3 years at 10% p.a. is Rs. 360. What would be the simple interest if the rate of interest will be 12% p.a. in five years ?**- Rs. 600
- Rs. 640
- Rs. 720
- Rs. 9000
- None of these
**On a certain sum of money the simple interest in 2 years at 12% p.a. is Rs. 120. What would be the simple interest if the rate of interest will be 15% p.a. in three years ?**- Rs. 216
- Rs. 225
- Rs. 240
- Rs. 250
- None of these
**On a certain sum of money the simple interest in 4 years at 10% p.a. is Rs. 480. What would be the additional simple interest if the rate of interest will be 12% p.a. in five years ?**- Rs. 216
- Rs. 225
- Rs. 240
- Rs. 576
- None of these

**:**

__Model 7__**The simple interest on Rs. 6400 at 12 1/2% per annum is Rs. 2000. Find the period ?**- 2 years
- 2 years 3 months
- 2 years 6 months
- 3 years 2 months
- None of these

**Solution :**

T = 100I / PR = (100 X 2000 X 2) / (6400 X 25) = 2 1/2 years

**Practice Problems on Model 7**

**The simple interest on Rs. 6000 at 12% per annum is Rs. 2280. Find the period ?**- 2 years
- 2 years 3 months
- 2 years 6 months
- 3 years 2 months
- None of these
**The simple interest on Rs. 8400 at 15% per annum is Rs. 2520. Find the period ?**- 2 years
- 2 years 3 months
- 2 years 6 months
- 3 years 2 months
- None of these
**The simple interest on Rs. 5400 at 16% per annum is Rs. 1944. Find the period ?**- 2 years
- 2 years 3 months
- 2 years 6 months
- 3 years 2 months
- None of these

__:__

**Model 8****The simple interest on Rs. 6000 in 3 years and 4 months is Rs. 3000. Find the rate percent per annum.**- 15
- 17.5
- 18
- 20
- None of these

**Solution :**

Here T = 3 4/12 = 3 1/3 = 10/3 years

We have to find out the rate

**R**I = PTR / 100 => R = 100I / PT

=> (100 X 3000 X 3) / (6000 X 10 ) = 15

**Practice Problems on Model 8 :**

**The simple interest on Rs. 6000 in 3 years and 3 months is Rs. 3900. Find the rate percent per annum.**- 15
- 17.5
- 18
- 20
- None of these
**The simple interest on Rs. 6000 in 4 years and 4 months is SR. 4680. Find the rate percent per annum.**- 15
- 17.5
- 18
- 20
- None of these
**The simple interest on Rs. 64000 in 4 years is RS. 4480. Find the rate percent per annum.**- 15
- 17.5
- 18
- 20
- None of these

__:__

**Model 9****Arjun took a loan of Rs. 4000 at S.I. After 2 years he cleared the loan by paying Rs. 5600. Find the rate % p.a.**- 12
- 12.5
- 15
- 18
- None of these

**Solution :**

Here Arjun took Rs. 4000 and Payed 5600. So the Interest will be 5600-4000 = 1600

So, R = 100I / PT

= (100 X 1600) / (400 X 2)

= 20

= (100 X 1600) / (400 X 2)

= 20

**Practice Problems on Model 9**

**Arjun took a loan of Rs. 4000 at S.I. After 3 years he cleared the loan by paying Rs. 5440. Find the rate % p.a.**- 12
- 12.5
- 15
- 18
- None of these
**Arjun took a loan of Rs. 4000 at S.I. After 2 years he cleared the loan by paying Rs. 5000. Find the rate % p.a.**- 12
- 12.5
- 15
- 18
- None of these
**Arjun took a loan of Rs. 4000 at S.I. After 4 years he cleared the loan by paying Rs. 6880. Find the rate % p.a.**- 12
- 12.5
- 15
- 18
- None of these

**:**

__Model 10__

**A lent Rs. 25000 to B for 4 years and Rs. 40000 to C for 3 1/2 year and got Rs. 24000 simple interest from both the cases. Find the rate p.c.p.a ?**- 9
- 10
- 12.5
- 15
- None of these

**Solution :**

Given that Σ [ (PTR)/100 ] = Rs. 24000

Σ [ (PTR)/100 ] = 250 x4R + 400x(7/2) R = 2400R

=> R = 10

**Practice Problems on Model 10**

**A lent Rs. 25000 to B for 4 years and Rs. 40000 to C for 3 years and got Rs. 27500 simple interest from both the cases. Find the rate p.c.p.a ?**- 9
- 10
- 12.5
- 15
- None of these
**A lent Rs. 25000 to B for 5 years and Rs. 40000 to C for 4 years and got Rs. 42750 simple interest from both the cases. Find the rate p.c.p.a**- 9
- 10
- 12.5
- 15
- None of these
**A lent Rs. 30000 to B for 4 years and Rs. 50000 to C for 3 years and got Rs. 24300 simple interest from both the cases. Find the rate p.c.p.a**- 9
- 10
- 12.5
- 15
- None of these

__:__

**Model 11****Ravi took a loan of Rs. 12000 at 12% p.a. Find the amount to be paid by him after 3 years at simple interest ?**- Rs. 4320
- Rs. 5600
- Rs. 17600
- Rs. 16320
- None of these

Here they asked amount. So, calculate the Interest and add it to Principle.

I = PTR/100 = 120 x 3 x 12 =4320

A = 4320 + 12000 = 16320

**Practice Problems on Model 11**

**Ram took a loan of Rs. 12600 at 12% p.a. Find the amount to be paid by him after 8 years at simple interest.**- Rs. 26596
- Rs. 25696
- Rs. 24696
- Rs. 26496
- None of these
**Teja took a loan of Rs. 22000 at 15% p.a. Find the amount to be paid by him after 2 years at simple interest.**- Rs. 26600
- Rs. 28800
- Rs. 26800
- Rs. 28600
- None of these
**Shiv took a loan of Rs. 35800 at 8% p.a. Find the amount to be paid by him after 5 years at simple interest.**- Rs. 51020
- Rs. 50120
- Rs. 52010
- Rs. 50210
- None of these

**Model 12****:**

**What sum will amount to Rs. 1920 in 4 years at 15% per annum simple interest ?**- Rs. 1200
- Rs. 1250
- Rs. 1320
- Rs. 1400
- None of these

**Solution :**

Interest = T x R = 4 x 15% = 60%

P = 100A / (100+TR) = (100 x 1920) / 160 = 1200

**Practice Problems on Model 12**

**What sum will amount to Rs. 1750 in 2 years at 20% per annum simple interest ?**- Rs. 1200
- Rs. 1250
- Rs. 1320
- Rs. 1400
- None of these
**What sum will amount to Rs. 11600 in 3 years at 15% per annum simple interest ?**- Rs. 8000
- Rs. 8800
- Rs. 9600
- Rs. 10000
- None of these
**What sum will amount to Rs. 16200 in 5 years at 7% per annum simple interest ?**- Rs. 9600
- Rs. 10000
- Rs. 11750
- Rs. 12000
- None of these

__:__

**Model 13****In how many years will a sum of money become double at 12 1/2% per annum simple interest ?**- 6
- 8
- 10
- 12
- None of these

**Solution :**

TR = 100

*x*- 100
T x 12 1/2 = 100 x 2 - 100

T x 25/2 = 100 = > T = 8

**Practice Problems on Model 13**

**In how many years will a sum of money become double at 8% per annum simple interest ?**- 6
- 8
- 10
- 12
- None of these
**In how many years will a sum of money become thrice at 12 1/2% per annum simple interest ?**- 6
- 8
- 10
- 12
- None of these
**In how many years will a sum of money become 2 1/2 times at 12 1/2% per annum simple interest ?**- 6
- 8
- 10
- 12
- None of these

__:__

**Model 14**

**A sum of money becomes double itself in 5 1/2 years at simple interest. In how many years will it becomes thrice ?**- 15
- 10
- 18
- 6
- None of these

**Solution :**

Rate is same for both the cases. So,

tr / TR = 100 (

*x*-1) / 100 (X-1)
=> t/T =

*x*-1 / X-1
here,

*x =*2, t = 5 1/2

X = 3, we have to find out T

=> (5 1/2) / T = 1/2 = > T = 11

**Practice Problems on Model 14**

**A sum of money becomes thrice itself in 10 years at simple interest. In how many years will it become 4 times ?**- 15
- 10
- 18
- 6
- None of these
**A sum of money becomes 2 1/2 time sitself in 12 years at simple interest. In how many years will it become 3 1/4 times ?**- 15
- 10
- 18
- 6
- None of these
**A sum of money becomes 1 3/4 times itself in 5 years at simple interest. In how many years will it become 5 1/2 times ?**- 15
- 20
- 18
- 25
- None of these

**:**

__Model 15__**A man received Rs. 240 as S.I. on Rs. 800 for 6 years. If he expects Rs. 300 as S.I on Rs. 1200, for how many years should he keep the deposit ?**- 4
- 4.5
- 5
- 7.5
- None of these

**Solution**:

r = R

100i / pt = 100I / PT

240 / (800x6) = 300 / 1200T

T = 5

**Practice Problems on Model 15**

**A man received Rs. 360 as S.I. on Rs. 1200 for 6 yars. If he expects Rs. 12000 as S. I on Rs. 4000, for how many years should he keep the deposit ?**- 4
- 4.5
- 5
- 7.5
- None of these
**A man received Rs. 720 as S.I on Rs. 4800 for 2 years. If he expects Rs. 1560 as S. I on Rs. 5200, for how many years should he keep the deposit ?**- 4
- 4.5
- 5
- 7.5
- None of these
**A man received Rs. 960 as S. I on Rs. 18000 for 3 years. If he expects Rs. 1440 as S. I on Rs. 10800 for how many years should he keep the deposit ?**- 4
- 4.5
- 5
- 135/16
- None of these

__:__

**Model 16****The S. I on a sum of money is 9/16 of the principal and the rate p.c.p.a is same as the number of years. Find the period.**- 4
- 4.5
- 5
- 7.5
- None of these

**Solution :**

I = 9/16 x P

=> I/P = 9/16

* If there is any relation between Time & rate TR = 100 I/P

Here time and rate are same

=> T x T = 100 x 9/16

=> T = 10 x 3/4 = 7 1/2 Years

**Practice Problems on Model 16**

**The S.I on a sum of money is 16/25 of the principal and the rate p.c.p.a is same as the number of years. Find the period.**- 4
- 4.5
- 5
- 7.5
- None of these
**The S.I on a sum of money is 8/25 of the principal and the rate p.c.p.a is twice as the number of years. Find the period.**- 4
- 4.5
- 5
- 7.5
- None of these
**The S.I on a sum of money is 9/10 of the principal and the rate p.c.p.a is two and a half times as the number of years. Find the rate.**- 6
- 9
- 12
- 15
- None of these

__:__

**Model 17****A certain sum amounts to Rs. 3120 in 3 years and to Rs. 4080 in 7 years. Find the rate p.c.p.a**- 9
- 10
- 12
- 15
- None of these

**Solution :**

Interest / 1 year = Difference in Amount / Difference in Time

= 960/4 = 240

P = 3120 - 3 x 240 = 2400

R = 100 I / PT = 100x240 / 2400x1 = 10

**Practice Problems on Model 17**

**A certain sum amounts to Rs. 6800 in 3 years and to Rs. 9800 in 8 years. Find the rate p.c.p.a.**- 9
- 10
- 12
- 15
- None of these
**A certain sum amounts to Rs. 4720 in 2 years and to Rs. 6880 in 8 years. Find the rate p.c.p.a.**- 9
- 10
- 12
- 15
- None of these
**A certain sum amounts to Rs. 9600 in 4 years and to Rs. 12300 in 7 years. Find the rate p.c.p.a.**- 9
- 10
- 12
- 15
- None of these

**Work with these models and solve the given practice problems. Share your solutions in the comments section below**.

**Will post shortcuts and Practice problems on Compound Interest tomorrow. All the Best :)**