(**Part IV**) consists of shortcut methods, tips and tricks to solve question from Probability, Banker’s Discount and Time and Distance. Now (**Part V**) includes another three very important section from quantitative aptitudes including *“Simple and Compound Interest”, “Partnership” and “Calendar”*.

Shortcut methods and tricks to solve questions from **Simple and Compound Interest** are given below:

**Simple Interest**

__Definition of Principal__

Certain amount of money borrowed for a certain time period is called **Principal or Sum**.

__Definition of Amount__

When simple interest is added to the Principal, the result is called the **Amount**

Amount (A) = S.I. (Simple Interest) + P (Principal)

S.I. = A – P

If P = Principal, R = Rate of Interest and T = Time in the Year, then

S.I = (P*R*T) / 100

P = (S.I*100) / ( R*T)

R = (S.I*100) / (P*T)

T = (S.I*100) / (P*R)

**Compound Interest (C.I)**

If P = Principal, R = Rate of Interest and T = Time in the Year, then the calculation of compound interest is as below:

__When interest is compounded annually__

Amount = P[1 + (R / 100)]^{T}

or C.I = Amount – P

__When interest is compounded Half-yearly__

Amount = P[1 + {R / (2 x 100)}]^{2T}

__When interest is compounded Quarterly__

Amount = P[1 + {R / (4 x 100)}]4^{T}

__When interest is compounded annually but time is in a fraction, as T(x/y) years, then__

Amount = P[1 + (R / 100)]^{T }x [1 + {(x/y) R} / 100)]

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Shortcut methods and tricks to solve questions from **‘Partnership’** are given below:

If a business or firm is run by the investment of more than one person’s agreement, then this kind of agreement is called Partnership.

There are two types of partners – **Sleeping** (invests but not get involved directly to run the firm or business) and **working** partners (invests and also get involved directly to run the firm or business).

There are two types of partnership – **Simple** (capitals of partners are invested for the same period of time) and **Compound** (capitals of partners are invested for the different period of time).

__Basic Formulas for Simple Partnership:__

(Capital of A / Capital of B) = (Profit of A / Profit of B)

(Capital of A : Capital of B) = (Profit of A : Profit of B)

__Basic Formulas for Compound Partnership:__

(Capital of A x Time Period of A / Capital of B x Time Period of B) = (Profit of A / Profit of B)

(Capital of A x Time Period of A : Capital of B x Time Period of B) = (Profit of A : Profit of B)

If n partners are investing for different period of time then,

C1T1: C2T2: C3T3: … : CnTn= P1: P2: P3: … : Pn

Rule 1

If two partners are investing their money X1 and X2 for equal period of time and their total profit is P then their shares of profit are:

(X1 x P) / (X1 + X2) and (X2 x P) / (X1 + X2)

If these partners are investing their money for different period of time which is T1 and T2, then their profits are:

(X1 x P x T1) / (X1T1 + X2T2) and (X2 x P xT2) / (X1T1 + X2T2)

Rule 2

If n partners are investing their money X1, X2, …, Xn for equal period of time and their total profit is P then their shares of profit are:

(X1 x P) / (X1 + X2+…………+Xn), (X2 x P) / (X1 + X2+…………+Xn), ……………………, ( Xn x P) / (X1 + X2+…………+Xn)

If these partners are investing their money for different period of time which is T1, T2,… , Tn then their profits are:

(X1 x T1 x P) / (XT1 + X2T2+…………+XnTn), (X2 x T2 x P) / (X1T1 + X2T2+…………+XnTn), ……………………, ( Xn x Tn x P) / (X1T1 + X2T2+…………+XnTn)

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Shortcut methods and tricks to solve questions from **‘Calendar’** are given below:

Odd Days

Number of days more than the complete weeks are called odd days in a given period

Leap Year

366 days year is a Leap year, where the February is of 29 days.

If a year is not a century, then every year divisible by 4 is a leap year.

**Examples:**

1948, 2012, 1684 etc. are leap years.

1993, 2007 etc. are not leap years.

Every 4th century is a leap year and no other century is a leap year.

**Examples:**

800, 1200, 1600 etc. are leap years.

200, 500, 700 etc. are not leap years.

Counting odd days and Calculating the day of any particular date

1 ordinary year ≡ 365 days ≡ (52 weeks + 1 day)

Hence number of odd days in 1 ordinary year= 1.

1 leap year ≡ 366 days ≡ (52 weeks + 2 days)

Hence number of odd days in 1 leap year= 2.

100 years ≡ (76 ordinary years + 24 leap years )

≡(76 x 1 + 24 x 2) odd days

≡ 124 odd days.

≡ (17 weeks + 5 days)

≡ 5 odd days.

Hence number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2) = 10 ≡ 3 odd days

Number of odd days in 300 years = (5 x 3) = 15 ≡ 1 odd days

Number of odd days in 400 years = (5 x 4 + 1) = 21 ≡ 0 odd days

Similarly, the number of odd days in all 4th centuries (400, 800, 1200 etc.) = 0

Mapping of the number of odd day to the day of the week is given below:

Last day of a century cannot be Tuesday or Thursday or Saturday.

For the calendars of two different years to be the same, the following conditions must be satisfied.

**1.** Both years must be of the same type. i.e., both years must be ordinary years or both years must be leap years.

**2.** 1st January of both the years must be the same day of the week.

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