Proportion:
The equality of two ratios is called proportion. The proportion of two ratios 2:3 & 12:18 means 2:3 = 12:18 and is written as:
2 : 3 :: 12 : 18, it is read as "2 ratio 3 is same as 12 ratio 18", and "::" is the proportion sign .
The numbers 2,3,12 &18 are called the terms of the proportion.2 is the first term,3 is the second term,12 is the third term and 18 is the forth term.
The first and forth terms are called "extremes". The third and second terms are called "means".
The product of means is always equal to the product of extremes. This property is used to find if any of the one term missing, by taking the cross product. Usually this unknown quantity is represented by x.

Examples:
1) Find the value of x if the following number is in proportion.
x : 4 :: 3 : 2
Product of extremes = 2x
Product of means = 12
2x = 12
x = 12 / 2
x = 6
The unknown value was 6 and the proportion was;
6 : 4 :: 3 : 2

2) If 20 meters of cloth cost $80,what will be the cost of 40 meters of cloth?
Let the cost 40 meters be x as it is the unknown quantity.So the proportion becomes,
20 : 80 :: 40 : x
Product of extremes = 20x
Product of means = 3200
20x = 3200
x = 3200 / 20
x = 160
40 meters will cost $160.

Partnership:
Two or more persons are said to entered into a partnership if they have contributed some mount of money in any business. This partnership is said to be simple if all the partners invest their money for equal duration of time. And the profit of such business is distributed depending on the ratio of the money invested by each member.

Examples:

1) A & B has started a business together ,by investing $200 and $300 respectively.If they get a profit of $50 in a month.What will each get?
Now $50 is to be distributed among them by the ratio 200 : 300 = 2 : 3.
Sum of ratio is 2 + 3 = 5.
A will get 2 / 5 * 50 = $20
B will get 3 / 5 * 50 = $30

2) X,Y & Z started a partnership by investing $6000, $5000,$3000,respectively. If they had a profit of $4500.What will each get?
Now the profit is to be divided according to their capital ie $6000, $5000,
and $3000 respectively.
Ratio of their profit = 6000 : 5000 : 3000
= 6 : 5 : 3
Sum of the ratios = 6 + 5 + 3 = 14
X will get = 6 / 14 * 4500
= $1928.58
Y will get = 5 / 14 * 4500
= $1607
Z will get = 3 / 14 * 4500
= $964.42

Inheritance:

Inheritance is the property, cash & other assets of a deceased person. This inheritance is divided among his near relation by the Law of Inheritance. The pupil among whom the property is divided, are the Heirs of the deceased.

Example:
1) Mr.S left inheritance of $ 4000.His widow got 1 / 8 of the property. The rest was distributed among his one son and one daughter. What is the share of each if the son gets twice than the daughter.
Total Amount = $4000
Share of widow = 1 / 8 ´ 4000
= $500
Ratio of son to daughter = 2 : 1
Sum of ratio = 2 + 1 = 3
Share of son = 2 / 3 ´ 3500 = $2333.334
Share of daughter = 3500 - 2333.334 = $1166.667

2) Mr. P suddenly died in a road accident. He left a property of worth $100000.According to his will, $3000 were distributed to poor. $1000 were given to one of his friends which he had borrowed few days before.1 / 8 of his remaining property was given to the widow. The rest was given to his 3 daughters and 2 sons. The ratio of the share son to daughter was 2 : 1. Find everyone's share?
Total Property = 100000$
Amount given to his friend = 1000$
Amount given to poor = 3000$
Remaining Amount = 100000 - 3000 - 1000 = 96000$
Share of his widow = 1 / 8 * 96000 = 12000$
Remaining amount = 96000 - 12000 = 84000$
Ratio of son to daughter = 2 : 1
Ratio = 1 : 1 : 1 : 2 : 2
Sum of ratio = 1 + 1 + 1 + 2 + 2 = 7
Each son's share = 2 / 7 ´ 84000 = 24000$
Each daughter's share = 1 / 7 ´ 84000 = 12000$

Unitary System:
In our daily life we are given the price of some articles and we are required to find the price of a number of that particular article so we use the unitary system. This is a special type of ratio and proportion.

Example:

1. If 25 kg of sugar cost 200$.What is the price of 10 kg?
Let the price of 10 kg be x
25 : 200 :: 10 : x
Product of Means = Product of Extremes
25x = 2000
x = 2000 / 25
x = 80$

2. If the price of 2 / 3 of the property is 1400$.What will be the price of 3 / 4 of the property.
Let the price of the 3 / 4 of the property be x.
2/3 : 1400 :: 3/4 : x
2/3 x = 3/4 ´ 1400
x = 3/2 x 3/4 ´ 1400
x = 1575$

 

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