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*. The person who shared*

**Anonymous***. Today I am going to share the*

**Mixture and Alligation Problems with Shortcut methods***. Hope it will help you. Happy Reading :)*

**Basics and Shortcut Methods of Simple and Compound Interest****P.S : Sorry for the bad handwriting :P**

**Interest**is the money paid for the use of money borrowed. The Sum borrowed is called the

**Principal**. The Sum of Interest and Principal is called the

**Amount**.

If the interest is paid as it falls due, it is called the

**Simple Interest (SI)**.
If P is the principal, R is the ratio; T is time and S.I is the Simple Interest, then,

Money is said to be lent at

**Compound Interest (C.I)**if the interest is not paid as soon as falls due, but is added to the Principal after a fixed period, so that the amount at the end of period becomes the principal for the next period. If A is the Amount, C.I is the Compound Interest, P is the Principal, R is the Rate, and t is the Time then,**Important Points to Note :**

- If Interest is paid half yearly; Time is doubled and the Rate is halved.
- If Interest is paid quarterly, time becomes 4 times
- Compound Interest for one year is equal to the Simple Interest for one year

**Difference Between Simple and Compound Interests**

For 2 years

For 3 years

Now let's do some example problems...

**Example 1**: A sum of money amounts to Rs. 944 in 3 years at a Simple Interest. If the ratio of interest be raised by 25% the sum amounts to 980 during the same period. Find the sum and the rate of interest.

**Solution :**

Rs. 980 - Rs. 944 = 36

Hence,

25% interest = Rs. 36

100% = (36 x 100) / 25 = Rs. 144

Hence the interest of three years = Rs. 144

Therefore,

Principal = 944 - 144 = Rs. 800

Rate = [(144 x 100) / (800 x 3)] = 6%

**Example 2**: Mahajan lends out Rs. 9 on the condition that the loan is payable in 10 months by 10 equal installments or Re. 1. Find the rate of percent per annum.

**Solution :**

Let the Interest be Rs.

*x*per month per rupee
Interest on Rs. 9 for 1 month = 9

*x*
Interest on Rs. 8 for 1 month = 8

*x*
Interest on Rs. 7 for 1 month = 7

*x*
Interest on Rs. 6 for 1 month = 6

*x*
Interest on Rs. 5 for 1 month = 5

*x*
Interest on Rs. 4 for 1 month = 4

*x*
Interest on Rs. 3 for 1 month = 3

*x*
Interest on Rs. 2 for 1 month = 2

*x*
Interest on Rs. 1 for 1 month = 1

*x*
Total Interest = 45

*x**But, according to the problem this must be Re. 1*

So, 45

*= 1 or**x**x =*1/45
Interest for 1 month on Re. 1 = 1/45

Interest for 12 month on Rs. 100 = (100 x 12)/45 => 85/3 => 26 (2/3) %

**Example 3 :**A man deposits Rs. 5,600 in a bank at 3(3/4) % annual interest. After 6 months he withdraws Rs. 3,200 together with interest and after 6 months the remaining money. How much does he get as Interest ?

Solution :

S.I for Rs. 5,600 for 6 months =

= Rs. 105

He withdraw Rs. 3,200 together with interest, the remaining amount = 5600 - 3200 = Rs. 2400

S.I on Rs. 2,400 at the rate of 15/4 for 1/2 years

= Rs. 45

So, Total Interest = 105 + 45 = Rs. 150

**Example 4 :**Find the Simple Interest on Rs. 5200 for 2 years at 6% per annum.

**Solution :**

Here P = Rs. 5,200, T = 2 years and R = 6%

=> Simple Interest = (P x R x T) / 100

= (5200 x 6 x 2) / 100

= Rs. 624

**Example 5**: Find the Simple Interest on Rs. 300 at 6% per annum from March 3rd to May 15th in the same year.

**Solution :**

Time from March 3rd to May 15th = 28 days of March + 30 days of April and 15 days of May

= 73 days = 73/365 years

= 1/5 years

=> S.I = (300 x 6 x 1/5) / 100

= Rs. 3.60

**Example 6 :**On what sum will the interest for 3 years at 4% per annum amount to Rs. 300 ?

**Solution :**

Here, T = 3 R = 4%

and S.I = 300

we need P

so P = (300 x 100) / (3x4)

= Rs. 2500

That's it for now guys. I will share few more example problems with solutions. Please let me know my way of explaining is understandable or not. So that I can improve. Good Day :)

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