Apptitude

## Calendar (How to Find day on Given Date)

Here we will deal with finding the day of the week on a particular date. The process lies on obtaining the no. of odd days.

Odd Days :- In a given period, number of days more than a complete weeks are called odd days.

Leap Year :- Every year which is divisible by 4 is called a leap year. Thus 1992,1996,2004 etc. are leap years. Every 4th century is a leap year like 400,800,1200 etc. but no other century is a leap year like 1500,1900,2100 etc.

An year which is not a leap year is called an ordinary year.

1. An ordinary year has 365 days.
2. A leap year has 366 days.

Counting of odd days :

1 ordinary year = 365 days

= 52 weeks + 1 day

= 1 odd day.

1 leap year = 366 days

= 52 weeks + 2 day

= 2 odd days.

100 years = 76 ordinary years + 24 leap years

= (76 x 52) + 76 days + (24 x 52) + 48 days

= 124 days = 124/7 = 5 odd days

100 years = 5 odd days

200 years = (5+5)/7 = 3 odd days

300 years = (5+5+5)/7 = 1 odd day

400 years = 21 = 0 odd days

(7n+m) odd days, where m<7 is equivalent to m odd days. Thus 8 odd days = 1 odd day.

Lets understand the concept of finding odd days and the day on a particular week by some examples.

Example :- What was the day on 15 August 1947 ?

Solution :- 15 august 1947 = (1946 years + Period from 1 january 1947 to 15 august 1947)

Counting of odd days: 1600 years + 300 years + 47 years

1600 years = 0 odd days.

300 years = 1 odd day.

47 years = 11 leap year + 36 ordinary year

= 11 x 2 + 36 = 58 = 58/7 = 2 odd days.

Jan.     Feb.      March        April       May       June     July        Aug.

31     +   28   +    31     +       30   +     31   +      30     +   31      +    15

= 227 days = 32 weeks + 3 days = 3 odd days

Total No. of odd days = 0+1+2+3 = 6 odd days

Hence , the required day was Saturday.

Example :- What was the day on 16 April 2000 ?

Solution = 16 April 2000 = (1999 year + Period from 1 january 2000 to 16 april 2000)

Counting of odd days:

1600 years + 300 years + 99 years

1600 years = 0 odd day.

300 year = 1 odd day

99 year = 24 leap year + 75 ordinary year

=(24 x 1 + 75 x 2)  = 123 odd days = 123/7 = 4 odd days

Jan.     Feb.      March        April

31     +   29  +    31     +       16

= 107 days = 15 weeks + 2 days = 2 odd days.

Total no. of odd days = 0+1+4+2 = 7 odd days = 0 odd days.

Hence, the required day was Monday.

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Apptitude

## Partnership

When two or more than two persons run a business together, they are called partners and the deal is known ad partnership.

1. Simple Partnership
2. Compound Partnership

Simple Partnership :- All the partners invest their capital or investment for same period of time.In this case profit earned is divided into the ratio of capital. Lets Understand with example :-

Example :- A and B started a business by investing Rs. 2000 and 3000 respectively for 1 year. Find the share of both, out of an annual profit of Rs. 2500.

Solution :- Here both have invested for same period of time so partnership is simple hence profit is divided into the ratio of capital

A:B = 2000:3000 =2:3

total ratio = 5

Profit of A = (2/5)*2500 = 1000

Profit of B = (3/5)*2500 = 1500

Compound Partnership :- All partners invest their capital for different period of time. Here profit in divided into the ratio of time value of money.

Time value of money = capital * time

Example :- A and B started a business by investing Rs. 2000 and 3000 respectively in which A invested for 1 year and B for half year. Find the share of both, out of an annual profit of Rs 3500.

Solution :- Here both have invested for different period of time so partnership is compound hence profit is divided into the ratio of time value of money

A:B = 2000*12 : 3000*6 =24000 : 18000 = 4:3

total ratio = 7

Profit of A = (3500/7)*4 = 2000

Profit of A = (3500/7)*3 = 1500

Working and Sleeping Partners :- A partner who manages the business is known as working partner and the one who simply invest money is a sleeping partner.

Working partner will get profit as well as salary whereas sleeping partner will only get profit no salary.

Lets Understand with an example:-

Example :- A and B started business by investing Rs. 100 and Rs 200 for same period of time but A is a active partner and B is sleeping partner and it was decided that 10 % of salary would be given to A.  Find the share of both, out of an annual profit of Rs 30.

Solution :-Annual profit = Rs 30

Salary of A = 10% of 30 = Rs 3.

Now profit = 30 -3 = Rs 27

Now profit is divided into the ratio of capital because both invested for same period of time.

A:B = 100 :200 = 1:2

total ratio = 3

Profit of A = [(1/3)*27 + 3] = 12

Profit of B = (2/3)*27 = 18

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